一类半线性热方程耦合系统的整体解

Global Solutions for a Coupled System of Semilinear Heat Equations

研究一类半线性热方程耦合系统带Dirichlet边界条件的问题 ,ut =vα1 uα2 (△u+u) , vt=uβ1 vβ2 (△v+v) , u =v Ω =0 ,u(x,0 ) =u0 (x) , v(x ,0 ) =v0 (x) (x∈Ω ,t>0 ) ,用正则化和上下解方法证明了该系统解的局部存在性 ,同时讨论了整体解的存在性 .

This paper deals with a coupled system of semilinear heat equations with Dirichlet boundary condition,u t=v α 1u α 2(△u+u), v t=u β 1v β 2(△v+v), u=v Ω=0, u(x,0)=u 0(x), v(x,0)=v 0(x)(x∈Ω,t>0).Local existence of a solution for the system is shown by using the regularization method and upper-lower solution technique. The global existence of a solution is discussed.