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 ($mgeq 2$) 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]. Submitted December 13, 2001. Published October 16, 2002. Math Subject Classifications: 35K45, 35K57. Key Words: Reaction diffusion systems; Lyapunov functionals; global existence
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