关键词: 四阶抛物方程, 径向解, 存在性

Abstract: We studied the radial symmetric solutions to the initial and boundary value problem of a fourth order nonlinear parabolic equation via the method of parabolic regularization and the Campanato framework and uniform Schauder type estimates, we obtained the existence of classical solutions for the regularized problem. On the basis of some necessary uniform estimates on the solutions of the regularized problem, we proved the existence of weak solutions.

Key words: fourth order parabolic equation, radial solution, existence