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

摘要

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