The Cauchy problem of the modified Helmholtz-type equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Thus the regularization methods are required to recover the numerical stability. In this paper, we propose a quasi-reversibility regularization method to deal with this ill-posed problem. Convergence estimates are obtained under a-priori bound assumptions for the exact solution and the selection of regularization parameter. Some numerical results are given to show that this method is stable and feasible.
机构:
Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
Hexi Univ, Dept Math, Zhangye City, Gansu, Peoples R ChinaLanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
Zhang, H. W.
Qin, H. H.
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机构:
Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R ChinaLanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
Qin, H. H.
Wei, T.
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Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R ChinaLanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
机构:
Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, NovosibirskSobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk
Romanov V.G.
Bugueva T.V.
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Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk
Novosibirsk State University, ul. Pirogova 2, NovosibirskSobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk
Bugueva T.V.
Dedok V.A.
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机构:
Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk
Novosibirsk State University, ul. Pirogova 2, NovosibirskSobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk
机构:
Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R ChinaLanzhou City Univ, Dept Math, Lanzhou 730000, Peoples R China
Qin, H. H.
Wen, D. W.
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机构:
Lanzhou City Univ, Dept Math, Lanzhou 730000, Peoples R China
Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R ChinaLanzhou City Univ, Dept Math, Lanzhou 730000, Peoples R China