Abstract

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.

Keywords: Reaction-diffusion system; global existence; Lyapunov functional.

MSC: 35K45, 35K57, 35K45

Pages:  274--282     

Volume  66 ,  Issue  3 ,  2014