International Journal of Differential Equations
Volume 2011 (2011), Article ID 831436, 24 pages
http://dx.doi.org/10.1155/2011/831436
Research Article

Weak Solution to a Parabolic Nonlinear System Arising in Biological Dynamic in the Soil

Côme Goudjo,1 Babacar Lèye,2 and Mamadou Sy2

1Département de Mathématiques, Faculté des Sciences, Université d'Abomey Calavi, Cotonou, Benin
2Laboratoire d'Analyse Numérique et Informatique (LANI), IRD, Antenne de Saint-Louis Université Gaston Berger de Saint-Louis, UFR SAT, Umi-Ummisco 209, BP 234 Saint-Louis, Senegal

Received 9 May 2011; Accepted 27 June 2011

Academic Editor: Elena I. Kaikina

Copyright © 2011 Côme Goudjo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a nonlinear parabolic system governing the biological dynamic in the soil. We prove global existence (in time) and uniqueness of weak and positive solution for this reaction-diffusion semilinear system in a bounded domain, completed with homogeneous Neumann boundary conditions and positive initial conditions.