Geodesic
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
Electronic journal of differential equations, Tome 2001 (2001)
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].
Classification : 35K45, 35K57
Keywords: reaction-diffusion systems, global existence, Lyapunov functional 
@article{EJDE_2001__2001__a151,
     author = {Kouachi,  Said},
     title = {Existence of global solutions to reaction-diffusion systems via a {Lyapunov} functional},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0989.35068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a151/}
}
TY  - JOUR
AU  - Kouachi,  Said
TI  - Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a151/
LA  - en
ID  - EJDE_2001__2001__a151
ER  - 
%0 Journal Article
%A Kouachi,  Said
%T Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a151/
%G en
%F EJDE_2001__2001__a151
Kouachi,  Said. Existence of global solutions to reaction-diffusion systems via a Lyapunov functional. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a151/