Regularity results for degenerate wave equations in a neighborhood of the boundary

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2022-09-05 DOI:10.3934/eect.2023013

Bruno S. V. Ara'ujo, R. Demarque, L. Viana

引用次数: 1

Abstract

In this paper we establish some regularity results concerning the behavior of weak solutions and very weak solutions of the degenerate wave equation near the boundary. For the nondegenerate case, the correponding results were originally obtained by Fabre and Puel (J. of Diff. Eq. 106, 1993). This kind of results is closely related to the exact boundary controllability for the wave equation as the limit of internal controllability.

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简并波动方程在边界附近的正则性结果

本文建立了简并波动方程在边界附近弱解和甚弱解行为的一些规律性结果。对于非简并情况，相应的结果最初由Fabre和Puel (J. of Diff. Eq. 106, 1993)得出。这种结果与波动方程作为内部可控性极限的精确边界可控性密切相关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology