A nonlinear damped transmission problem as limit of wave equations with concentrating nonlinear terms away from the boundary

In this paper we study an initial and boundary value problem for damped wave equations with nonlinear singular terms concentrating away from the boundary of the domain, on an interior neighbourhood of a hyper-surface M that collapses to M as ɛ goes to zero. We describe the conditions for well posedn...

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Bibliographic Details
Published in:	Nonlinear analysis Vol. 241; p. 113492
Main Authors:	Jiménez-Casas, Ángela, Rodríguez-Bernal, Aníbal
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01-04-2024
Subjects:	Concentrating terms Damped wave equation Singular limit Transmission problem Transmission problem 35L71 35L81 Singular limit 35L05 Damped wave equation Concentrating terms 35L20
Online Access:	Get full text
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Summary:	In this paper we study an initial and boundary value problem for damped wave equations with nonlinear singular terms concentrating away from the boundary of the domain, on an interior neighbourhood of a hyper-surface M that collapses to M as ɛ goes to zero. We describe the conditions for well posedness of both the approximating and limit problems, as well as the convergence, at the singular limit, of the solutions of the former to solutions of the latter, when the parameter ɛ goes to zero.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2024.113492