Global existence and boundedness of solutions for a general activator-inhibitor model

Abstract

The purpose of this paper is to prove global existence in time of solutionsfor a class of multi-component reaction diffusion systems called multipleGierer-Meinhardt type. The system describes, following Gierer-Meinhardt'sscheme, "m'' substances in interaction. The nonlinearities present adifficulty since they are fractions. We prove the global existence by usinga series of Lyapunov functionals.