四阶非线性抛物方程解之存在性

四阶椭圆方程解之极值原理最先由Dunninger,D.R.提出.Goyal,V.B.和Singl,K.P.推广到半线性方程的情形,文献[5]、[6]作进一步的推广,都对文献[3]的某些结论作了修正,并且都建立四阶椭圆方程边值问题解的存在性定理。关于四阶抛物方程解的极值原理及唯一性定理作者作过讨论。这篇短文研究四阶非线性抛物方程的初值问题和混合问题解的存在性,其前提是所有解的最大模有一致先验的上界。

The Existence of Solutions of The Nonlinear Fourth-order Parabolic Equations

In this note, initial value problems (16) (17)and mixed boundary value problems (23) (24) (25 )bor non-linear parabolic equations are discurred. By means of the schauder type estimates of the linear parabolic equtions and the embedding theorem in Nikol'skii spaces, we show that these problems have Aolutions inthe space H^4-a?(4+a)/2(D_n-1^T)(H^4+a?(4-a)/2)Q^T