Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation
Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation
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非线性演化方程的存在性及其在简并抛物方程中的应用
DOI：
10.1155/2014/567241
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Li Zhang
中科院分区：
文献类型：
--
作者：
S. Ning;Li Zhang
本文考虑一类双非线性发展方程的抽象Cauchy问题，其中是一个真实的自反Banach空间，是从到其对偶的极大单调算子（可能是多值的）。考虑到一些实际应用，我们假设和是次微分。利用后差逼近，建立了存在性，证明依赖于的连续性和的连续性。作为应用，我们给出了一个非线性退化抛物型方程解的存在性。
We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form in , , where is a real reflexive Banach space, and are maximal monotone operators (possibly multivalued) from to its dual . In view of some practical applications, we assume that and are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of and the coerciveness of . As an application, we give the existence for a nonlinear degenerate parabolic equation.