Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation

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http://hdl.handle.net/10138/326780

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Korpela , J , Lassas , M & Oksanen , L 2019 , ' Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation ' , Inverse problems and imaging , vol. 13 , no. 3 , pp. 575-596 . https://doi.org/10.3934/ipi.2019027

Title: Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation
Author: Korpela, Jussi; Lassas, Matti; Oksanen, Lauri
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Matti Lassas / Principal Investigator
University of Helsinki, Department of Mathematics and Statistics
Date: 2019-06
Language: eng
Number of pages: 22
Belongs to series: Inverse problems and imaging
ISSN: 1930-8337
URI: http://hdl.handle.net/10138/326780
Abstract: An inverse boundary value problem for the 1+1 dimensional wave equation (partial derivative(2)(t) - c(x)(2)partial derivative(2)(x))u(x,t) = 0, x is an element of R+ is considered. We give a discrete regularization strategy to recover wave speed c(x) when we are given the boundary value of the wave, u(0,t), that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed (c) over tilde, satisfying a Holder type estimate parallel to (c) over tilde - c parallel to
Subject: Inverse problem
regularization theory
wave equation
discretization
ILL-POSED PROBLEMS
NONLINEAR TIKHONOV REGULARIZATION
BANACH-SPACES
RECONSTRUCTION
DIRICHLET
STABILITY
RECOVERY
UNIQUENESS
ALGORITHM
THEOREM
111 Mathematics
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