Global solution of reaction diffusion system with non diagonal matrix

Demonstratio mathematica

article

Abdelkader Moumeni¹  Lylia Salah Derradji¹ 

[1] Laboratoire de Mathématiques, Université Badji Mokhtar

关键词: reaction diffusion systems;    global existence;    Lyapunov functional;   

DOI  :  10.1515/dema-2013-0366

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

The purpose of this paper is to prove the global existence in time of solutions for the coupled reaction-diffusion system: {∂u∂t−aΔu−bΔv=f (u, v)in ]0, +∞[×Ω∂u∂t−cΔv=g(u,v)in ]0, +∞[×Ω**487**$$\left\{ {\matrix{{{{\partial u} \over {\partial t}} - a\Delta u - b\Delta v = f\,(u,\,v)} \hfill & {{\rm in}\,]0,\, + \infty [ \times \Omega } \hfill \cr {{{\partial u} \over {\partial t}} - c\Delta v = g(u,v)} \hfill & {{\rm in}\,]0,\, + \infty [ \times \Omega } \hfill } } \right.$$ with triangular matrix of diffusion coefficients. By combining the Lyapunov functional method with the regularizing effect, we show that global solutions exist. Our investigation applied for a wide class of the nonlinear terms f and g .

【 授权许可】

CC BY