A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions
type: Item
instance of: scholarly article
title: A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions
zbMATH Open document ID: 1329.35181
author: Lorena Bociu
author: J. P. Zolesio
published in: Journal of Differential Equations
publication date: 2015-09-22T00:00:00Z
review text: An IBV problem for the linear inhomogeneous wave equation with mixed (Dirichlet and Neumann) boundary conditions is analyzed. Actually, one considers a zero Dirichlet boundary condition on a part of the boundary and a non-smooth Neumann boundary condition on the remainder of the boundary of the domain. Under a special assumption on interior and boundary data, the existence, uniqueness and interior regularity of solution is proved. For the proof, standard Galerkin approximation technique is used. Under additional assumptions on interior and boundary data, hidden boundary regularity for the solution of the wave equation is proved. For the proof, one introduces the so called pseudo-extractor technique which makes use of the Fourier transform and shape optimization techniques.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6484221
zbMATH Keywords: Dirichlet boundary condition
zbMATH Keywords: Neumann boundary condition
zbMATH Keywords: Galerkin approximation
zbMATH Keywords: shape optimization techniques
MaRDI profile type: Publication
full work available at URL: j.jde.2015.07.006
OpenAlex ID: W2209214169
Wikidata QID: Q57435073
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DOI: 10.1016/J.JDE.2015.07.006
description: scientific article; zbMATH DE number 6484221