Existence of global solutions to reaction-diffusion systems via a Lyapunov functional

The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations) which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11]