## Differential and Integral Equations

### Global existence and large time behavior of positive solutions to a reaction diffusion system

#### Abstract

We consider a reaction diffusion system whit a triangular matrix of diffusion coefficients satisfying a balance law on a bounded domain with no-flux boundary condition. We demonstrate that globally bounded solutions exist for any reaction term provided a condition on the diffusion coefficients is satisfied. The proof makes use of some properties of the Neumann function for the heat equation posed in a bounded domain recently obtained in [12]. When the spatial domain is {\rm \bf R}$^N$, the proof relies on well-known properties of the fundamental solution of the heat equation.

#### Article information

Source
Differential Integral Equations, Volume 13, Number 1-3 (2000), 255-264.

Dates
First available in Project Euclid: 21 December 2012