Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume 37, Issue 1, Pages 24-43Publisher
WILEY
DOI: 10.1002/num.22517
Keywords
inverse initial value problem; iterative Tikhonov regularization method; time-fractional diffusion-wave equation; uniqueness
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Funding
- National Natural Science Foundation of China [11371181, 11601207, 11771192, 11871392]
- Fundamental Research Funds for the Central Universities [lzujbky-2020-12]
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This study introduces a method to recover two initial values for a time-fractional diffusion-wave equation, achieving uniqueness by Laplace transformation and analytic continuation, followed by solving the inverse problem using an iterative Tikhonov regularization method and proposing a finite dimensional approximation algorithm for finding good approximations to the initial values. Numerical examples in one- and two-dimensional cases demonstrate the effectiveness of the proposed method.
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.
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