一类非线性退化抛物方程有界弱解的存在性

Existence of Bounded Weak Solutions for a Class of Nonlinear Degenerate Parabolic Equations

本文主要研究一类非线性退化抛物型方程,其中主算子在解为无穷大时退化非强制,即当解u趋于无穷时,扩散现象消失。利用先验估计方法和经典的紧性理论,得到了解的L∞估计,并由此证明了有界弱解的存在性。

This paper deals with a class of nonlinear degenerate parabolic equations whose main operators goes to zero as the solution tends to infinity,when the solution of u tends to infinity,the diffusion phenomenon disappears. Using a priori estimation method and classical compactness theory,we obtain the L∞estimates for the solutions,and then prove the existence of bounded weak solutions to such problems.