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




Kouachi, Said

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Southwest Texas State University, Department of Mathematics


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].



Reaction diffusion systems, Lyapunov functionals, Global existence


Kouachi, S. (2002). Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional. <i>Electronic Journal of Differential Equations, 2002</i>(88), pp. 1-13.


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