A unified framework for parabolic equations with mixed boundary conditions and diffusion on interfaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Disser, Karoline¹  Meyries, Martin²  Rehberg, Joachim¹ 

[1] Karl Weierstrass Inst Math, D-10117 Berlin, Germany

[2] Univ Halle Wittenberg, Inst Math, D-06099 Halle, Saale, Germany

关键词: Parabolic equations;    Dynamical boundary conditions;    Degenerate diffusion;    Surface diffusion;    Power weights;    Lipschitz domain;   

DOI  :  10.1016/j.jmaa.2015.05.041

来源: Elsevier

【 摘 要 】

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-infinity-calculus for the corresponding operator, providing well-posedness for a large class of initial conditions and external forces. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free