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Li, Xiao-Xiao; Yang, Fan; Liu, Jie; Wang, Lan

The quasireversibility regularization method for identifying the unknown source for the modified Helmholtz equation. (English) Zbl 1266.35144

J. Appl. Math. 2013, Article ID 245963, 8 p. (2013).
Summary: This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the quasireversibility regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

Cited in 1 Document

MSC:

35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
93B30 System identification
65F22 Ill-posedness and regularization problems in numerical linear algebra
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\textit{X.-X. Li} et al., J. Appl. Math. 2013, Article ID 245963, 8 p. (2013; Zbl 1266.35144)
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References:

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