Observability of the 1-D wave equation with mixed boundary conditions in a non-cylindrical domain
type: Item
instance of: scholarly article
title: Observability of the 1-D wave equation with mixed boundary conditions in a non-cylindrical domain
zbMATH Open document ID: 1395.35135
author: Abdelmouhcene Sengouga
published in: Mediterranean Journal of Mathematics
publication date: 2018-06-01T00:00:00Z
review text: The homogeneous, one space dimension, wave equation with mixed boundary conditions, i.e. Neumann type condition at \(x=0\) and Dirichlet condition at moving point \(x=lt\) is considered. Under some assumptions, one proves the existence and uniqueness of a solution and one obtains the exact solution developed in a series. Further, energy estimates and observability at the endpoints \(x=0\) and \(x=lt\) are investigated. Results on existence and uniqueness of solution as well as energy estimates and observability at endpoints are shown also for the reversed mixed boundary conditions, that is Dirichlet condition at \(x=0\) and Neumann type condition at the moving point \(x=lt\).
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 93B07
zbMATH DE Number: 6879902
zbMATH Keywords: generalized Fourier series
MaRDI profile type: Publication
full work available at URL: s00009-018-1107-y
OpenAlex ID: W2794328537
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DOI: 10.1007/S00009-018-1107-Y
description: scientific article; zbMATH DE number 6879902