一类高阶半线性抛物型方程初值问题解

Solutions of Cauchy Problem for a Class of Hign Order Semilinear Parabolic Equations

本文讨论了方程(1):+(-Δ)=F(u,D_z,…,)和方程(2):+(-Δ)=F的初值问题,在关于幂性非线性项F=O(||~1+)a≥1为整数的假定之下,对方程(1),在x的维数n>2m/a的条件下,对方程(2),在x维数n≥1的任意情形,论证了小初值问题在时间大范围的可解性,唯一性,基于线性方程解的衰减估计和能量估计,所设计的某种Sobolev空间上的压缩映象原理.

This paper is concerned with the global existencs (in time) of solutions to semilinear parabolic equa- tions u_t+(-Δ)()u=F(u,D_u,…,D^(2m)u) with small initial data,where F satisfies some power-type condi- tion.We obtain global existence(in time) results for the above mentioned Cauchy problem.The methods used here are due to Ii Ta-tsien and chen Yun-mei.