Wavelet regularization for an inverse heat conduction problem.
type: Item
instance of: scholarly article
title: Wavelet regularization for an inverse heat conduction problem.
zbMATH Open document ID: 1055.35139
author: Chuli Fu
author: You-Bin Zhu
author: Chunyu Qiu
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-26T00:00:00Z
review text: The goal of this paper is to consider the following nonstandard inverse heat conduction problem in the quarter plane (\(t\geq 0\), \(x\geq 0\)): \[ \begin{cases} u_t+ u_x= u_{xx},\quad & x\geq 0,\;t\geq 0,\\ u(x,0)= 0,\quad & x\geq 0,\\ u(1,t)= g(t),\quad & t\geq 0,\end{cases}\tag{1} \] where \(g\in L^2(0,\infty)\) is the temperature history at the fixed point \(x= 1\). The authors look for such a solution \(u(x,\cdot)\in L^2(0,\infty)\) which is bounded as \(x\to\infty\) and they give out a wavelet regularization method for (1) with strict proof.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 2032584
zbMATH Keywords: Ill-posed problem
zbMATH Keywords: Inverse heat conduction problem
zbMATH Keywords: Meyer wavelets
zbMATH Keywords: Regularization
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.08.003
OpenAlex ID: W1976610400
cites work: Q3771806
cites work: Determining Surface Temperatures from Interior Observations
cites work: Sideways heat equation and wavelets
cites work: Q4545721
cites work: Wavelet and Fourier Methods for Solving the Sideways Heat Equation
cites work: Ten Lectures on Wavelets
DOI: 10.1016/J.JMAA.2003.08.003
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description: scientific article; zbMATH DE number 2032584