Doubly nonlinear evolution equations with non‐monotone perturbations
Doubly nonlinear evolution equations with non‐monotone perturbations
复制标题
具有非单调扰动的双非线性演化方程
DOI：
10.1002/pamm.200700647
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
G. Akagi
中科院分区：
文献类型：
--
作者：
G. Akagi
在适当的假设下，证明了自反Banach空间中具有非单调扰动的双非线性抽象发展方程Cauchy问题强解的局部（在时间上）存在性.为了证明存在性，引入了几个近似问题，并使用凸分析和Kakutani‐Ky Fan不动点定理的各种工具讨论了精细的极限过程。最后给出了上述抽象理论在非线性偏微分方程中的应用。（© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
The local (in time) existence of strong solutions to Cauchy problems for doubly nonlinear abstract evolution equations with non‐monotone perturbations in reflexive Banach spaces is proved under appropriate assumptions, which allow the case where solutions of the corresponding unperturbed problem may not be unique. To prove the existence, a couple of approximate problems are introduced and delicate limiting procedures are discussed by using various tools from convex analysis and the Kakutani‐Ky Fan fixed point theorem. Furthermore, an application of the preceding abstract theory to a nonlinear PDE is also given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)