Geodesic
Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Most publications on reaction-diffusion systems of $m$ components ($m\geq 2$) impose $m$ inequalities to the reaction terms, to prove existence of global solutions (see Martin and Pierre [10] and Hollis [4]). The purpose of this paper is to prove existence of a global solution using only one inequality in the case of 3 component systems. Our technique is based on the construction of polynomial functionals (according to solutions of the reaction-diffusion equations) which give, using the well known regularizing effect, the global existence. This result generalizes those obtained recently by Kouachi [6] and independently by Malham and Xin [9].
Classification : 35K45, 35K57
Keywords: reaction diffusion systems, Lyapunov functionals 
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     author = {Kouachi, Said},
     title = {Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a {Lyapunov} functional},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a27/}
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Kouachi, Said. Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a27/