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
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摘要: 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。Abstract: 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.