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Preprint . 2022
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zbMATH Open
Article . 2023
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Evolution Equations and Control Theory
Article . 2023 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2022
License: CC BY
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Regularity results for degenerate wave equations in a neighborhood of the boundary

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2023Embargo end date: 01 Jan 2022Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Evolution Equations and Control Theory, volume 12, pages 1,300-1,315 (eissn: 2163-2480, Copyright policy )
Authors: Araújo, Bruno S. V.; Demarque, Reginaldo; Viana, Luiz;

doi: 10.3934/eect.2023013 , 10.48550/arxiv.2209.02108

arXiv: 2209.02108

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

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.

Related Organizations
Keywords

degenerate operator, regularity of solutions, Smoothness and regularity of solutions to PDEs, Asymptotic behavior of solutions to PDEs, behavior near the boundary, 35L05, 35L80, 35B65, 35B40, Mathematics - Analysis of PDEs, Degenerate hyperbolic equations, FOS: Mathematics, Wave equation, wave equation, Initial-boundary value problems for second-order hyperbolic equations, Analysis of PDEs (math.AP)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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