Asymptotic behaviour of global solutions to a model of cell invasion

In this paper we analyze a mathematical model focusing on key events of the cells invasion process. Global well-possedness and asymptotic behaviour of nonnegative solutions to the corresponding coupled system of three nonlinear partial differential equations are studied.Comment: 29 page

Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours

In this paper we consider a nonlinear system of differential equations arising in tumour invasion which has been proposed in [1] M.A.J. Chaplain and A.R.A. Anderson, Mathematical modelling of tissue invasion, in Cancer Modelling and Simulation, ed., L. Preziosi (Chapman & Hall/CRT, 2003), pp. 269–297. The system consists of two PDEs describing the evolution of tumour cells and proteases and an ODE which models the concentration of the extracellular matrix. We prove local existence and uniqueness of solutions in the class of Hölder spaces. The proof of local existence is done by Schauder’s fixed point theorem and for the uniqueness we use an idea from [2] H. Gajewski, K. Zacharias, Global behaviour of a reaction-diffusion system modelling chemotaxis, Math. Nachr. 195 (1998) 77–114.Marie Curie Research Training Networ

On some models describing cellular movement: The macroscopic scale

Along this work we will consider several models of partial differential equations that describe cellular movement. We will introduce some mathematical techniques in order to describe the behaviour of the solutions of these models.Junta de Andalucí

Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions

A system of quasilinear non-uniformly parabolic-elliptic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The proof of existence and uniqueness of a global-in-time weak solution is given. First the local solutions are constructed. This is done by the Schauder fixed point theorem. Uniqueness is proved with the use of the duality method. A priori estimates are stated either in the case when the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened.Marie Curie Research Training Networ

Convergencia al equilibrio en un modelo simplificado de angiogénesis

En esta comunicación abordamos una clase general de modelos con origen en biología. En particular los modelos describen el movimiento de bacterias, procesos invasivos tumorales y el proceso de angiogénesis asociado a los tumores

Global solutions and asymptotic behavior for a parabolic degenerate coupled system arising from biology

In this paper we will focus on a parabolic degenerate system with respect to unknown functions u and w on a bounded domain of the two-dimensional Euclidean space. This system appears as a mathematical model for some biological processes. Global existence and uniqueness of a nonnegative classical Hölder continuous solution are proved. The last part of the paper is devoted to the study of the asymptotic behavior of the solutions.Dirección General de Enseñanza Superio

Uniqueness of solution for elliptic problems with non-linear boundary conditions

In this paper we present results of uniqueness for an elliptic problem with nonlinear boundary conditions.Ministerio de Ciencia y Tecnologí

Anti-angiogenic therapy based on the binding receptors

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 specific receptors of the endothelial cells. We study the time-dependent problem as well as the stationary problem associated to it.Ministerio de Ciencia e Innovació