On ill-posedness and a Tikhonov regularization for a multidimensional inverse hyperbolic problem
type: Item
instance of: scholarly article
title: On ill-posedness and a Tikhonov regularization for a multidimensional inverse hyperbolic problem
zbMATH Open document ID: 0885.35146
author: M. Yamamoto
published in: Journal of Mathematics of Kyoto University
publication date: 1998-04-23T00:00:00Z
review text: The author considers the initial/boundary value problem for the wave equation in a bounded domain \(\Omega\subset\mathbb{R}^r\) with a source term of the kind \[ \lambda(t)f(x),\quad \lambda\in C^1[0, T],\quad \lambda(0)\neq 0,\quad f\in L^2(\Omega). \] He studies the inverse problem of determining \(f\) from Neumann boundary data on \(\partial\Omega\) and investigates questions of existence, uniqueness, stability, and stable reconstruction using Tikhonov's regularization.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35R25
zbMATH DE Number: 1062469
zbMATH Keywords: source determination
zbMATH Keywords: wave equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: stability
zbMATH Keywords: reconstruction
zbMATH Keywords: Tikhonov regularization
reviewed by: Gottfried Bruckner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518455
OpenAlex ID: W1573978674
DOI: 10.1215/KJM/1250518455
description: scientific article; zbMATH DE number 1062469