Geodesic
Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions
Electronic journal of differential equations, Tome 2002 (2002)
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 = {Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     doi = {10.14232/ejqtde.2002.1.2},
     zbl = {0988.35078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14232/ejqtde.2002.1.2/}
}
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Kouachi,  Said. Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions. Electronic journal of differential equations, Tome 2002 (2002). doi: 10.14232/ejqtde.2002.1.2

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