Abstract

RUIZ VERA, Jorge Mauricio. A convergent iterative method for a logistic chemotactic system. Rev.colomb.mat. [online]. 2017, vol.51, n.1, pp.103-117. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v51n1.66843.

In this paper we study a nonlinear system of differential equations arising in chemotaxis. The system consists of a PDE that describes the evolution of a population and another which models the concentration of a chemical substance. In particular, we prove the existence and uniqueness of nonnegative solutions via an iterative method. First, we generate a Cauchy sequence of approximate solutions from a linear modification of the original system. Next, some uniform bounds on the solutions are used to find a subsequence that converges weakly to the solution of the original system.

Keywords : reaction-diffusion equations; weak solution; convergence.

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