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Selecciones Matemáticas
Academic Journal Academic Journal | 30/01/2018 Please log in to see more details
Selecciones Matemáticas
30/01/2018

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math - applied mathematics - mathematical analysis - algebra - geometry - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Local Well-posedness of a Nutku-Oguz-Burgers System With Time Dependent Coefficients
Juan Montealegre;Gladys Cruz
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 121-136 (2018) Please log in to see more details
In this paper we study the local well-posedness of the initial value problem for a Nut... more
Local Well-posedness of a Nutku-Oguz-Burgers System With Time Dependent Coefficients
Selecciones Matemáticas, Vol 5, Iss 02, Pp 121-136 (2018)
In this paper we study the local well-posedness of the initial value problem for a Nutku-Oguz-Burgers system with time dependent coefficients, formed by two Korteweg-de Vries equations coupled through the non-linear terms. The system appears as a model of wave propagation in a shallow channel with variable bottom surface, in which both nonlinear and dispersive effects are relevant. The proof of existence and uniqueness of local solution and the continuous dependence on the initial data of the local solution in Sobolev spaces Hs(R)xHs(R), s > 3/2, are based on the works [9] and [17]

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Initial alue problem - Korteweg-de Vries equations - Local well-posedness - Sobolev Spaces - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Transversal Intersection Curves of Two Surfaces in Minkowski 3-Space
Osmar Alêssio;Sayed A.-N. Badr;Soad A. Hassan;Luciana A. Rodrigues;Fábio N....
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 137-153 (2018) Please log in to see more details
In this paper, we study the differential geometry of the transversal intersection curv... more
Transversal Intersection Curves of Two Surfaces in Minkowski 3-Space
Selecciones Matemáticas, Vol 5, Iss 02, Pp 137-153 (2018)
In this paper, we study the differential geometry of the transversal intersection curve of two surfaces in Minkowski 3-space, where each pair satisfies the following types spacelike-lightlike, timelike-lightlike and lightlike-lightlike. Surfaces are generally give by their parametric or implicit equations, then the surfacesurface intersection problem appear commonly as parametric-parametric, parametric-implicit and implicitimplicit. We derive the Frenet frame, Darboux frame, curvature, torsion, normal curvature and geodesic curvatures of transversal intersections for all types of intersection problems. We show the intersection curve may be spacelike (timelike, lightlike or pseudo null) curve. Finally, we show our methods by given several examples.

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Minkowski 3-Space - Surface-Surface intersection - Pseudo null curve - Null curve - Null frame - Lightlike surface - Darboux Frame - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Existencia de solución débil para un problema no lineal con el operador p-Laplaciano fraccionario
Raúl Sánchez A.;Cesar Torres
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 154-163 (2018) Please log in to see more details
We study the existence of weak solution for a non-linear problem with fractional p-Lap... more
Existencia de solución débil para un problema no lineal con el operador p-Laplaciano fraccionario
Selecciones Matemáticas, Vol 5, Iss 02, Pp 154-163 (2018)
We study the existence of weak solution for a non-linear problem with fractional p-Laplacian operator for the case where the order of the fractional derivative is 1/p J(tu), where J is the functional associated to the non-linear problem to be studied, the main result is obtained.

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Fractional Calculus - Nehari Manifold - Fibering Maps - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Modelo Huésped-Vector: Análisis de estabilidad y simulaciones
Jhelly Reynaluz Pérez Núñez;Luis Javier Vásquez Serpa
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 175-192 (2018) Please log in to see more details
In epidemiological mathematics, the SIR model is well known, as well as the diseases t... more
Modelo Huésped-Vector: Análisis de estabilidad y simulaciones
Selecciones Matemáticas, Vol 5, Iss 02, Pp 175-192 (2018)
In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease.

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Epidemiology - SIR model - host model - vector - vital dynamics - Runge – Kutta - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Decaimiento Polinomial y Modelaje Numérico Computacional de la viga de Timoshenko con disipación parcial
Frank Henry Acasiete Quispe;Neisser Pino Romero
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 164-174 (2018) Please log in to see more details
We studied the uniform stabilization of a class of Timoshenko systems with partial dis... more
Decaimiento Polinomial y Modelaje Numérico Computacional de la viga de Timoshenko con disipación parcial
Selecciones Matemáticas, Vol 5, Iss 02, Pp 164-174 (2018)
We studied the uniform stabilization of a class of Timoshenko systems with partial dissipation of the beam. Our main result is to prove that the semigroup associated to this model has polynomial decay. Moreover, we prove that the semigroup decays polynomially to zero. The system decays polynomially with rate depending on the coeficients of the problem. We also show the computational modeling of the system showing the results obtained theoretically.

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Differential partial equations - beam - semigroup - polynomial stability - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Congruencias de esferas geodésicas em H3 e S3
Edwin O. S. Reyes;Carlos M. C. Riveros
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 212-229 (2018) Please log in to see more details
In [2], was obtained a characterization of the surfaces in R3 which are envelopes of a... more
Congruencias de esferas geodésicas em H3 e S3
Selecciones Matemáticas, Vol 5, Iss 02, Pp 212-229 (2018)
In [2], was obtained a characterization of the surfaces in R3 which are envelopes of a sphere congruence in R3, in which the other envelope is in R2. In this paper, we characterize the surfaces of H3 and S3 which are envelopes of a congruence of geodesic spheres in H3 and S3, respectively, in which the other envelope is contained in H2⊂H3 and S2⊂S3. We show that this characterization allows locally to obtain a parameterization of the surfaces contained in H3 and S3, this characterization extends the result obtained in [2]. Moreover, we provide sufficient conditions for these surfaces to be locally associated by a transformation of Ribaucour. Also, we present families of surfaces parameterized by lines of curvature in H3 and S3, which depend on a function of two variables which is solution of a differential equation. Finally, we characterize the surfaces of the spherical type ∑ in H3 and S3, as the surfaces where its radius function is the solution of the Helmholtz equation.

Subject terms:

Surfaces of the spherical type - lines of curvature - Hyperbolic space - congruence of geodesic spheres - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Desingularización de Superficies Casi Ordinarias Irreducibles
Rina Roxana Paucar Rojas
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 230-240 (2018) Please log in to see more details
The aim of this work is to study and describe the resolution or desingularization of i... more
Desingularización de Superficies Casi Ordinarias Irreducibles
Selecciones Matemáticas, Vol 5, Iss 02, Pp 230-240 (2018)
The aim of this work is to study and describe the resolution or desingularization of irreducible quasi ordinary surfaces, following Lipman’s approach ( [6], [7]). To achieve our goal, we define the quasi ordinary surfaces and describe their parametrization by quasi ordinary branches, we also define the quasi ordinary rings, local rings of the quasi ordinary irreducible surfaces, then we study the relationship that exists between the tangent cone and singular locus of a quasi ordinary ring and the distinguished pairs of a quasi ordinary normalized branch that represents this ring. Also, we define the special transforms of a quasi ordinary ring and show that they are again quasi ordinary.

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quasi ordinary algebroid surfaces - resolution of singularities - blowups - quasi ordinary rings - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Simulación Numérica de Ondas Viajeras del Sistema FitzHugh-Nagumo
C. E. Rubio-Mercedes;Glauce Barbosa Verao
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 193-203 (2018) Please log in to see more details
The FitzHugh-Nagumo system has a special type of solution called traveling wave, which... more
Simulación Numérica de Ondas Viajeras del Sistema FitzHugh-Nagumo
Selecciones Matemáticas, Vol 5, Iss 02, Pp 193-203 (2018)
The FitzHugh-Nagumo system has a special type of solution called traveling wave, which has the form u(x, t) =f(x − μt) and w(x, t) =g(x − μt), which is a stable solution over time. Our interest is to numerically characterize the profile of a traveling wave (f-g) and its propagation speed μ(t). With a change of variables, we transform the problem of finding the solutions in original coordinates to a problem of finding the equilibria in a new coordinate system called mobile coordinates or non-local coordinate system. aa With numerical examples we will demonstrate that the solutions of the system of EDPs in non-local coordinates converge to a traveling wave of the original problem. The non-local coordinate system also allows to calculate the exact propagation speed.

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Traveling wave - Stable solution - PDEs - Mobile coordinates - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Minimización y Maximización de Funciones Casisupermodulares
Nelson Aragonés Salazar
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 204-211 (2018) Please log in to see more details
This article presents some properties of the casisupermodular function and demonstrate... more
Minimización y Maximización de Funciones Casisupermodulares
Selecciones Matemáticas, Vol 5, Iss 02, Pp 204-211 (2018)
This article presents some properties of the casisupermodular function and demonstrates principles of discarding to solve the problem of minimization and maximization of this type of function defined in the family of subsets of a given finite set (finite boolean lattice); these principles are generalized, in the case of minimization, to a relatively complemented finite lattice. This work extends some results obtained by V.R. Khachaturov and R.V. Khachaturov for the case of supermodular functions.

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Combinatorial optimization - quasi-supermodular function - supermodular function - finite lattice - boolean lattice - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Sobre el Espacio Euclidiano Bidimensional
Edgar Vera Saravia;Henry Zubieta Rojas
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 241-248 (2018) Please log in to see more details
We offer a geometric introduction to the two-dimensional Euclidean Space E2 using both... more
Sobre el Espacio Euclidiano Bidimensional
Selecciones Matemáticas, Vol 5, Iss 02, Pp 241-248 (2018)
We offer a geometric introduction to the two-dimensional Euclidean Space E2 using both the geometric approach of the affine R-Space and the two-dimensional Geometric Algebra. These notes, intented for university proffessors of physics and mathematics, try to emulate the program developed by Felix Kline in the first decade of the 20th century.

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Geometric Algebra - Euclidean Space - Afin Space - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Un Modelo Matemático para la Circulación Oceánica en el Fenómeno de El Niño
Obidio Rubio;Ruth Noriega
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 5, Iss 02, Pp 249-264 (2018) Please log in to see more details
We describe a model that interprets the circulation of the tropical ocean in the perio... more
Un Modelo Matemático para la Circulación Oceánica en el Fenómeno de El Niño
Selecciones Matemáticas, Vol 5, Iss 02, Pp 249-264 (2018)
We describe a model that interprets the circulation of the tropical ocean in the periods when the meteorological phenomenon known as ”El Ni˜no” appears; A study area is defined as being the equatorial pacific, the ocean current is described by the primitive equations, which consists of the equations of motion and temperature transport which are strongly coupled. As boundary conditions, the wind stresses on the surface of the ocean is fundamental for the warming of waters, which due to its high variability we consider it random and described by a multiplicative white noise, generating the so-called stochastic primitive equations for the circulation of the tropical ocean. The variational formulation of the problem is presented and some estimates that allow verifying the existence of solutions of these equations.

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Phenomenon El Niño - Primitive Equations - Stochastic Systems - Tropical Ocean - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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El problema de Cauchy para la ecuación de Korteweg-De Vries en espacios de Bourgain
Cesar Loza Rojas
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 2, Pp 162-174 (2017) Please log in to see more details
En este artículo, estudiamos el problema de Cauchy a la ecuación de Korteweg-De Vries ... more
El problema de Cauchy para la ecuación de Korteweg-De Vries en espacios de Bourgain
Selecciones Matemáticas, Vol 4, Iss 2, Pp 162-174 (2017)
En este artículo, estudiamos el problema de Cauchy a la ecuación de Korteweg-De Vries en Hs con s >-3/4. Para ello utilizamos los espacios de Bourgain, Xs;b, y obtenemos buena formulación local al problema de Cauchy.

Subject terms:

Teorema de existencia local y unicidad - transformaciones integrales - aplicaciones de EDP en áreas distintas de la física - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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An alternative approach to the power series method
Márcio Rostirolla Adames
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 2, Pp 139-151 (2017) Please log in to see more details
This article consider the classical problem of linear non-homogeneous second order Ini... more
An alternative approach to the power series method
Selecciones Matemáticas, Vol 4, Iss 2, Pp 139-151 (2017)
This article consider the classical problem of linear non-homogeneous second order Initial Value Problems with analytic coefficients. It classifies the possible kinds of analytic solutions, giving criteria for the nonexistence of analytical solutions and for the existence of multiple analytic solutions. An alternative proof for the convergence of the power series method is given and it applies for some singular irregular points.

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ODE - Non-homogeneous - Initial Value Problem - Power Series - Strong Operator Convergence - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Hypersurfaces with planar lines of curvature in Euclidean Space
Carlos M. C. Riveros;Armando M. V. Corro
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 2, Pp 152-161 (2017) Please log in to see more details
In this work, we present explicit parameterizations of hypersurfaces parameterized by ... more
Hypersurfaces with planar lines of curvature in Euclidean Space
Selecciones Matemáticas, Vol 4, Iss 2, Pp 152-161 (2017)
In this work, we present explicit parameterizations of hypersurfaces parameterized by lines of curvature with prescribed Gauss map and we characterize the hypersurfaces with planar curvature lines. As an application we obtain a classification of isothermic surfaces with respect to the third fundamental form with two planar curvature lines. Also, we present a class of surfaces with one family of planar curvature lines and generalize these results to present classes of hypersurfaces with families of planar curvature lines.

Subject terms:

Sphere congruence - Laplace invariants - lines of curvature - isothermic surfaces - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Processos de Hawkes: Uma Modelagem do Book de Oferta no Mercado Acionário Brasileiro
Yuri Sampaio Maluf;Cira E. Guevara Otiniano
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 38-50 (2017) Please log in to see more details
Neste artigo é abordado o processo de Hawkes na modelagem do Book de oferta, em especi... more
Processos de Hawkes: Uma Modelagem do Book de Oferta no Mercado Acionário Brasileiro
Selecciones Matemáticas, Vol 4, Iss 1, Pp 38-50 (2017)
Neste artigo é abordado o processo de Hawkes na modelagem do Book de oferta, em especial o fundo de índice ETF iShare Ibovespa. O estudo teve como objetivo investigar a dinamica das influencias das ofertas em relacao as ordens passadas, além da interacao das taxas de ordens dos lados opostos do Book. Outro ponto tratado é a verificacao da estratégia de operacao que capte a dinámica estudada. No primeiro momento, foi realizada a abordagem univariada e no segundo a multivariada do processo de Hawkes. Os resultados mostram que em ambos os casos os dados se ajustaram bem ao processo de Hawkes. Os modelo ajustado indica que os agentes possuem comportamentos similares quando atuam como compradores ou como vendedores de ativos. Quanto a estratégia, nao foi possível estabelecer ganhos sobressalentes a partir das mudancas nas taxas de ofertas. No entanto, estes resultados se devem mais ao bid-ask spread do que a capacidade preditiva das funcaos intensidades .

Subject terms:

Processos Pontuais - Processo de Hawkes - Book de Oferta - ETF - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Ciclos límites en modelos depredador-presa
Liliana Puchuri Medina
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 70-81 (2017) Please log in to see more details
El modelo clásico de Lotka-Volterra pertenece a una familia de ecuaciones diferenciale... more
Ciclos límites en modelos depredador-presa
Selecciones Matemáticas, Vol 4, Iss 1, Pp 70-81 (2017)
El modelo clásico de Lotka-Volterra pertenece a una familia de ecuaciones diferenciales denominada “Lotka-Volterra generalizado”, que forma parte de una clasificación de cuatro modelos de campos cuadráticos con centro. Estos modelos han sido estudiados para responder el problema infinitesimal de Hilbert, que consiste en determinar el número de ciclos límites que posee un sistema hamiltoniano perturbado y con centro. En este trabajo, en primer lugar presentamos una prueba alternativa de la existencia de centros en el modelo depredador-presa de Lotka-Volterra. Esta nueva prueba se basa en ecuaciones algebraicas dadas por Kapteyn, que surgieron para responder al problema de Poincaré para campos cuadráticos. En segundo lugar, usando el teorema de la bifurcación de Hopf, probamos que modelos depredador-presa más realistas, obtenidos por una pertubación no lineal del modelo de Lotka-Volterra clásico, poseen ciclos límites.

Subject terms:

Ciclos límites - centro - campos hamiltonianos - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Calibración numérica de leyes de conservación escalar vía un algoritmo genético continuo
Stefan Berres;Aníbal Coronel;Richard Lagos
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 16-24 (2017) Please log in to see more details
En este artículo se investiga sobre el problema de la identicación de parámetros del f... more
Calibración numérica de leyes de conservación escalar vía un algoritmo genético continuo
Selecciones Matemáticas, Vol 4, Iss 1, Pp 16-24 (2017)
En este artículo se investiga sobre el problema de la identicación de parámetros del flujo en una ley de conservación escalar. El problema es formulado como un problema de optimización, donde la función objetivo compara la solución del problema directo con el perfil observado en un tiempo fijo. Un esquema de volúmenes finitos resuelve el problema directo y un algoritmo genético continuo resuelve el problema inverso. El método numérico es vericado con datos experimentales sintéticos. Los parámetros simulados se recuperan aproximadamente. La técnica de optimización heurística probada resulta ser más robusta que las técnicas clásicas de optimización.

Subject terms:

algoritmo genetico - identicacion del ujo - Volumen finito - algoritmo genético - identificación del flujo - ley de conservación - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Cocientes de variedades por acciones de grupos reductivos
Nélida Medina García
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 25-29 (2017) Please log in to see more details
Consideramos el anillo de polinomios R = K[x1, . . . , xn] en las variables x1, . . . ... more
Cocientes de variedades por acciones de grupos reductivos
Selecciones Matemáticas, Vol 4, Iss 1, Pp 25-29 (2017)
Consideramos el anillo de polinomios R = K[x1, . . . , xn] en las variables x1, . . . , xn y coeficientes complejos. El grupo de permutaciones de 1, . . . , n actúa sore R permutando las variables. El conjunto de invariantes por esta acción forma un anillo generado por los polinomios simétricos elementales. Emmy Noether prueba que si un grupo finito de matrices inversibles G ⊂ GL(n; k) actúa sobre R, entonces el anillo de invariantes es generado por un número finito de invariantes homogéneos y define un operador en G para obtener polinomios invariantes. Existen relaciones algebraicas entre los generadores del anillo de invariantes y las órbitas de Cn/G. En 1963, Masayoshi Nagata demostró que el anillo de los invariantes de los grupos geométricamente reductivos es finitamente generado. Analizamos la existencia de una variedad cociente X/G donde G es un grupo algebraico actuando sobre una variedad algebraica X.

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Variedades - Grupos reducidos - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Invariantes de Laplace en hipersupercies parametrizadas por líneas de curvatura
Armando M. V. Corro
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 30-37 (2017) Please log in to see more details
En este trabajo, usando la teoría de invariantes de Laplace damos otra demostración de... more
Invariantes de Laplace en hipersupercies parametrizadas por líneas de curvatura
Selecciones Matemáticas, Vol 4, Iss 1, Pp 30-37 (2017)
En este trabajo, usando la teoría de invariantes de Laplace damos otra demostración del siguiente resultado: Una hipersupercie de Dupin própia Mn para n ≥ 4 en Rn+1 con n curvaturas principales distintas y curvatura de Mobius constante, no puede ser parametrizada por líneas de curvatura. También, estudiamos clases especiales de hipersupercies Mn; n ≥ 3; en Rn+1, parametrizadas por líneas de curvatura con n curvaturas principales distintas y obtenemos una relación geométrica cuando los invariantes de Laplace son nulos, mostramos que las foliaciones de Mn son hipersupercies umbílicas si y solamente si mijk = 0. Además, las foliaciones de Mn son hipersupercies de Dupin si y solamente si mij = 0.

Subject terms:

Invariantes de - Invariantes de Laplace - hipersuperficies de Dupin - líneas de curvatura - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Eigenvalues of truncation matrix associated to the transition operator of the adding machine in base 2
Ali Messaoudi;Rafael Asmat Uceda
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 59-69 (2017) Please log in to see more details
In this work we build the stochastic adding machine in base 2 considering the truncati... more
Eigenvalues of truncation matrix associated to the transition operator of the adding machine in base 2
Selecciones Matemáticas, Vol 4, Iss 1, Pp 59-69 (2017)
In this work we build the stochastic adding machine in base 2 considering the truncation matrix Sn associated to the operator S and we study the eigenvalues of the matrix Sn acting in l∞(N).

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Stochastic - adding machine - eigenvalues - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Existence of three solution for fractional Hamiltonian system
César Torres Ledesma;Oliverio Pichardo Diestra
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 51-58 (2017) Please log in to see more details
In this paper we consider the fractional Hamiltonian system... more
Existence of three solution for fractional Hamiltonian system
Selecciones Matemáticas, Vol 4, Iss 1, Pp 51-58 (2017)
In this paper we consider the fractional Hamiltonian system...

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Fractional calculus - fractional derivatives - fractional Hamiltonian system - boundary value problem - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Existencia global y explosión de la solución de un problema de difusión - reacción
Julio Becerra Saucedo
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 82-101 (2017) Please log in to see more details
En este artículo se hace un estudio analítico sobre la existencia global y local de la... more
Existencia global y explosión de la solución de un problema de difusión - reacción
Selecciones Matemáticas, Vol 4, Iss 1, Pp 82-101 (2017)
En este artículo se hace un estudio analítico sobre la existencia global y local de la solución de un problema de difusión - reacción. Se demuestra que si la solución existe localmente entonces ésta llega a explotar en tiempo finito. Este resultado se extiende al caso en que la solución exista globalmente. Se llega a concluir que el tiempo máximo de existencia de la solución depende del dominio, del término que representa la reacción en la ecuación y de una función prueba definida en este trabajo. Así mismo se plantea la posibilidad de extender la existencia local a global usando el concepto de solución propia.

Subject terms:

problema de difusión - reacción - existencia global - existencia local - solución explosiva - tiempo de explosión - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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Mathematical analysis of a food chain: prey - predator - biological - control
Jhelly Pérez Nuñez;Roxana López Cruz
Academic Journal Academic Journal | Selecciones Matemáticas, Vol 4, Iss 1, Pp 112-123 (2017) Please log in to see more details
In this work, we present the dynamics of biological control through a mathematical mod... more
Mathematical analysis of a food chain: prey - predator - biological - control
Selecciones Matemáticas, Vol 4, Iss 1, Pp 112-123 (2017)
In this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent predator-prey model with Holling type II functional response, adding a top predator so this model is a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundary of solutions. The information given in this work could also be useful for the design of development plans that meet the needs of the agricultural sector to guide the non-pollution of the environment in the country through the use of biological control to control pests.

Subject terms:

Predator - Prey - Food Chain - Biological Control - Scenarios Extinction - Asymptotic Stability - Runge - Kutta - Applied mathematics. Quantitative methods - T57-57.97 - Mathematics - QA1-939

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