Existence of Global Solutions to Reaction-Diffusion Systems with Nonhomogeneous Boundary Conditions via a Lyapunov Functional

Abstract

Most publications on reaction-diffusion systems of m components (m ≥ 2) impose m inequalities to the reaction terms, to prove existence of global solutions (see Martin and Pierre [10] and Hollis [4]). The purpose of this paper is to prove existence of a global solution using only one inequality in the case of 3 component systems. Our technique is based on the construction of polynomial functionals (according to solutions of the reaction-diffusion equations) which give, using the well known regularizing effect, the global existence. This result generalizes those obtained recently by Kouachi [6] and independently by Malham and Xin [9].