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Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation
Author(s) -
Zhang Yun,
Wei Ting,
Zhang YuanXiang
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22517
Subject(s) - tikhonov regularization , mathematics , continuation , uniqueness , mathematical analysis , laplace transform , regularization (linguistics) , inversion (geology) , inverse problem , cauchy distribution , diffusion equation , wave equation , initial value problem , boundary value problem , paleontology , economy , structural basin , artificial intelligence , computer science , economics , biology , programming language , service (business)
This study is devoted to recovering two initial values for a time‐fractional diffusion‐wave equation from boundary Cauchy data. We provide the uniqueness result for recovering two initial values simultaneously by the method of Laplace transformation and analytic continuation. And then we use a nonstationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm to find good approximations to the initial values. Numerical examples in one‐ and two‐dimensional cases are provided to show the effectiveness of the proposed method.