MBE
A therapy inactivating the tumor angiogenic factors
Cristian Morales-Rodrigo
Mathematical Biosciences & Engineering 2013, 10(1): 185-198 doi: 10.3934/mbe.2013.10.185
This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. The main feature of the model under consideration is a nonlinear flux production of tumor angiogenic factors at the boundary of the tumor. It is proved the global existence for the nonlinear system and the effect in the large time behavior of the system for high doses of the therapeutic agent.
keywords: Chemotaxis anti-angiogenic therapy.
DCDS-B
Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient
Giovany M. Figueiredo Tarcyana S. Figueiredo-Sousa Cristian Morales-Rodrigo Antonio Suárez
Discrete & Continuous Dynamical Systems - B 2017, 22(11): 1-23 doi: 10.3934/dcdsb.2018311

In this paper we study a stationary problem arising from population dynamics with a local and nonlocal variable diffusion coefficient. We show the existence of an unbounded continuum of positive solutions that bifurcates from the trivial solution. The global structure of this continuum depends on the value of the nonlocal diffusion at infinity and the relative position of the refuge of the species and of the sets where it diffuses locally and not locally, respectively.

keywords: Bifurcation method variable local and nonlocal diffusion coefficient
CPAA
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.
DCDS
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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