A widely convergent method for determining the distributed parameters of the elliptical equation
type: Item
instance of: scholarly article
title: A widely convergent method for determining the distributed parameters of the elliptical equation
zbMATH Open document ID: 0789.65088
DOI: 10.1016/0096-3003(94)90100-7
author: Bo Han
author: Jiqun Shao
author: Baoqi Guo
published in: Applied Mathematics and Computation
publication date: 1994-04-10T00:00:00Z
review text: The authors study identification problems in elliptic partial differential equations. More precisely, the following equation defined on the time-space domain is considered \(L(a(x),t)u(x,t) = 0\) where \(a(x_ 1,\dots,x_ p)\) is the unknown operator to be identified. Of course initial and boundary conditions are given: \(Eu(x,0) = g(x)\); \(Bu(x,t) = f(x,t)\) on the boundary; \(Au(x,t) = \varphi(x,t)\) on a part of the boundary. A nonlinear operator \(Q\) is introduced: \(Q(a,t) = Au(a;x,t) - \varphi(x,t)\) and the inverse problem is stated as the following nonlinear operator equation: (1) \(Q(a,t) = 0\). The principle of continuation homotopy is used for solving (1) associated to a Newton-like method. Numerical results are given. Reviewer's remark: For this kind of problem I suggest to use a decomposition method (Adomian's technique) allowing to obtain \(u(x,t)\) in function of \(a(x)\) explicitly.
reviewed by: Yves Cherruault
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 519651
zbMATH Keywords: parameter identification
zbMATH Keywords: numerical results
zbMATH Keywords: elliptic partial differential equations
zbMATH Keywords: inverse problem
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: principle of continuation homotopy
zbMATH Keywords: Newton-like method
MaRDI profile type: Publication
full work available at URL: 0096-3003(94)90100-7
OpenAlex ID: W2004421894
cites work: Iterative algorithms for nonlinear problems in remote sensing
cites work: A Generalized Pulse-Spectrum Technique (GPST) for Determining Time-Dependent Coefficients of One-Dimensional Diffusion Equations
cites work: An Iterative Algorithm for Solving Inverse Problems of Two-Dimensional Diffusion Equations
cites work: Iterative Solution of Nonlinear Equations in Several Variables
Recommended article: Application of the decomposition method to identify the distributed parameters of an elliptical equation
Recommended article: A family of ellipse methods for solving non-linear equations
Recommended article: Q4849580
Recommended article: Ellipsoidal estimation on solutions to differential equations by means of matrix comparison systems
Recommended article: A note on the elliptic equation method
Recommended article: On the influence of parameters on the solvability of some conjugate problems for elliptical equations
Recommended article: On the Least-Squares Method for Elliptically Contoured Distributions
Recommended article: Q3363188
Recommended article: Q3696454
Recommended article: An elliptic equation method and its applications in nonlinear evolution equations
description: scientific article; zbMATH DE number 519651