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


Said Kouachi




The purpose of this paper is to prove global existence in time of solutions for a class of multi-component reaction diffusion systems called multiple Gierer-Meinhardt type. The system describes, following Gierer-Meinhardt's scheme, ``m'' substances in interaction. The nonlinearities present a difficulty since they are fractions. We prove the global existence by using a series of Lyapunov functionals.