A unified framework for parabolic equations with mixed boundary conditions and diffusion on interfaces
A unified framework for parabolic equations with mixed boundary conditions and diffusion on interfaces
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DOI：
10.1016/j.jmaa.2015.05.041
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发表时间：
2013-12
期刊：
影响因子：
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通讯作者：
K. Disser;M. Meyries;J. Rehberg
中科院分区：
文献类型：
--
作者：
K. Disser;M. Meyries;J. Rehberg
本文考虑一般非光滑情形下的标量抛物型方程，着重讨论界面条件和混合边界条件。特别是，我们研究动力学和扩散的Lipschitz接口和边界上，扩散系数仅假设是有界的，可测的和半正定的。在散装，我们认为扩散系数可能退化到Lipschitz表面。对于这类问题，我们引入了一个统一的基于半双线性形式的泛函分析框架，并给出了相应算子的极大Lp正则性和有界H∞演算，为一类初始条件和外力提供了适定性.
In this paper we consider scalar parabolic equations in a general non-smooth setting emphasizing interface conditions and mixed boundary conditions. In particular, we study dynamics and diffusion on a Lipschitz interface and on the boundary, where the diffusion coefficients are only assumed to be bounded, measurable and positive semidefinite. In the bulk, we consider diffusion coefficients which may degenerate towards a Lipschitz surface. For this problem class, we introduce a unified functional analytic framework based on sesquilinear forms and show maximal L p-regularity and bounded H∞-calculus for the corresponding operator, providing well-posedness for a large class of initial conditions and external forces.