The truncation regularization method for identifying the initial value of heat equation on a spherical symmetric domain
type: Item
instance of: scholarly article
title: The truncation regularization method for identifying the initial value of heat equation on a spherical symmetric domain
zbMATH Open document ID: 1414.65016
author: Fan Yang
author: Ya-Ru Sun
author: Xiao-Xiao Li
author: Chengye Ma
published in: Boundary Value Problems
publication date: 2018-12-20T00:00:00Z
review text: The inverse problem of identifying the initial value for the heat equation with inhomogeneous source on a spherical symmetric domain is investigated. The authors consider an inhomogeneous heat equation on a symmetric domain as follows: \[ \begin{cases} u_t- \frac{2}{r} u_r - u_{rr}=f(r,t), \ \ &0<t<T, \ 0<r<r_0,\\ u(r,0)= \varphi(r), \ \ &0 \leq r \leq r_0,\\ u(r_0,t)=0, \ \ &0 \leq t \leq T,\\ u(r,t) \text{ is bounded},\ \ &0<t<T,\ 0<r< r_0. \end{cases} \] The additional condition $u(r, T)=g(r)$ is used to determine the initial condition $\varphi(r)$. \par The truncation regularization method (the projection regularization method) is used for solving the inverse problem. The convergence of the approximate solutions to the exact solution under a priori and a posteriori regularization parameter choice rules is proved. A numerical example is presented to validate the effectiveness of this method.
reviewed by: Elena V. Tabarintseva
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35R25
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 6996321
zbMATH Keywords: inverse problem
zbMATH Keywords: ill-posed problem
zbMATH Keywords: spherical symmetric domain
zbMATH Keywords: truncation method
zbMATH Keywords: identifying initial value
MaRDI profile type: Publication
full work available at URL: s13661-018-0934-x
OpenAlex ID: W2787958589
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DOI: 10.1186/S13661-018-0934-X
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description: scientific article; zbMATH DE number 6996321