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

Bruno S. V. Araújo; Reginaldo Demarque; Luiz Viana

doi:10.3934/eect.2023013

Article Contents

2023, Volume 12, Issue 5: 1300-1315. Doi: 10.3934/eect.2023013

This issue Previous Article Null boundary controllability for some biological and chemical diffusion problems Next Article Analysis and simulation of an adhesive contact problem governed by fractional differential hemivariational inequalities with history-dependent operator

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

1.
Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Campina Grande, PB, Brazil
2.
Departamento de Ciências da Natureza, Universidade Federal Fluminense, Rio das Ostras, RJ, Brazil
3.
Departamento de Análise, Universidade Federal Fluminense, Niterói, RJ, Brazil

^*Corresponding author: Reginaldo Demarque
^*Corresponding author: Reginaldo Demarque

Received: September 2022

Revised: February 2023

Early access: March 29, 2023

Published online: March 29, 2023

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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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Mathematics Subject Classification: Primary: 35L05, 35L80; Secondary: 35B65, 35B40.

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References

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