A logistic equation with degenerate diffusion and Robin boundary conditions
Antonio Suárez
Communications on Pure & Applied Analysis 2008, 7(5): 1255-1267 doi: 10.3934/cpaa.2008.7.1255
In this paper we study a model for a species confined in a bounded region. This species diffuses slowly, follows a logistic law in the habitat and there is a flux of population across the boundary of the habitat.
Basically, we give some theoretical results of the model depending on some parameters which appear in the model.
keywords: Logistic equation bifurcation methods. degenerate diffusion Robin boundary conditions
Biodiversity and vulnerability in a 3D mutualistic system
Giovanny Guerrero José Antonio Langa Antonio Suárez
Discrete & Continuous Dynamical Systems - A 2014, 34(10): 4107-4126 doi: 10.3934/dcds.2014.34.4107
In this paper we study a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative relation with plants. We compare the dynamical properties of this system with the associated one under absence of the pollinator. We observe how cooperation is a common fact to increase biodiversity, which it is known that, generically, holds for general mutualistic dynamical systems in Ecology as introduced in [4]. We also give mathematical evidence on how a cooperative species induces an increased biodiversity, even if the species is push to extinction. For this fact, we propose a necessary change in the model formulation which could explain this kind of phenomenon.
keywords: increasing biodiversity 3D mutualistic model global stability. permanence vulnerability
Some eigenvalue problems with non-local boundary conditions and applications
Rafael Abreu Cristian Morales-Rodrigo Antonio Suárez
Communications on Pure & Applied Analysis 2014, 13(6): 2465-2474 doi: 10.3934/cpaa.2014.13.2465
In this paper we study an elliptic eigenvalue problem with non-local boundary condition. We prove the existence of the principal eigenvalue and its main properties. As consequence, we show the existence and uniqueness of positive solution of a nonlinear problem arising from population dynamics.
keywords: Non-local boundary condition eigenvalue problem.
Anti-angiogenic therapy based on the binding to receptors
Manuel Delgado Cristian Morales-Rodrigo Antonio Suárez
Discrete & Continuous Dynamical Systems - A 2012, 32(11): 3871-3894 doi: 10.3934/dcds.2012.32.3871
This paper deals with a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to specific receptors of the endothelial cells. We study the time-dependent problem as well as the stationary problem associated to it.
keywords: Chemotaxis anti-angiogenic therapy bifurcation.

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