一类半线性抛物型方程混和问题整体弱解的存在性

The Existence of Global Weak Solutions for the Initial-boundary Value Problem in a Kind of Semi-linear Parabolic Equations

运用Galerkin方法并结合势井理论,证明了一类半线性抛物型方程ut-Δu+up=0的高维情形的初边值混和问题在t 0的整体弱解的存在性.对于p为奇数的情形,容易得到先验估计,主要考虑p不是奇数时的情形,并得到相应的结果.

The Galerkin method, together with the potential well （stable set） method, is employed to solve the existence of global weak solutions of the primary limit value of a kind of semi-linear parabolic equations ： in case of high dimension when . It is easy to get prior estimation when p is odd. Thus, this paper focuses on the situation when p is not odd and gets corresponding results.