Generalized Tikhonov-type regularization method for the Cauchy problem of a semi-linear elliptic equation

This paper considers the Cauchy problem of a semi-linear elliptic equation and uses a generalized Tikhonov-type regularization method to overcome its ill-posedness. The existence, uniqueness, and stability for regularized solution are proven. Under an a priori bound assumption for exact solution, we...

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Bibliographic Details
Published in:	Numerical algorithms Vol. 81; no. 3; pp. 833 - 851
Main Authors:	Zhang, Hongwu, Zhang, Xiaoju
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.07.2019 Springer Nature B.V
Subjects:	Algebra Algorithms Cauchy problems Computer Science Convergence Eigenvalues Exact solutions Helmholtz equations Integral equations Iterative methods Numeric Computing Numerical Analysis Original Paper Regularization Regularization methods Stability Theory of Computation Semi-linear elliptic equation Ill-posed problem Convergence estimate Generalized Tikhonov-type regularization method Cauchy problem
ISSN:	1017-1398, 1572-9265
Online Access:	Get full text
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