关于半线性抛物型方程的整体可解性

On Global Solvability of Semiliaear Parabolic Equations

本文研究半线性抛物型方程u_t=△u+f(x,t,u,Du)的第一边值问题的整体可解性,主要讨论f中含有Du的高于二次增长的情形。得出在适当条件下该问题的整体可解性。

In this paper, We study the global solvability of first boundary value problem of semilinear parabolic equation ut=△u+f(x,t,u,Du).We discuss the case that f contains the |Du|. in which S≥2 and obtain under proper conditions the global solvability of this probleem.