一类非线性退化抛物方程解的存在性与正则性

Existence and Regularity of Solutions to a Class of Nonlinear Degenerate Parabolic Equations

摘要: 本文主要研究一类非线性退化抛物方程，其中方程的主算子在解u趋于无穷时退化非强制 (亦即当解u趋于无穷时，扩散现象消失)。通过取适当的试验函数，利用先验估计方法和经典的紧性理论，证明了问题弱解的存在性与正则性。

Abstract: This paper studies a class of nonlinear degenerate parabolic equations, in which the main operators goes to zero as the solution u tends to infinity (that is, the diffusion goes to zero when u goes to infinity). By choosing a suitable test function using a priori estimation method and compactness theory, the existence and regularity of weak solutions to the problem are proved.