The Backward Problem for Nonlinear Fractional Diffusion Equation with Time-Dependent Order

This paper investigates the nonlinear backward fractional diffusion equations (BFDEs) having a variable order and variable diffusion coefficient. It is well-known that the BFDEs are ill-posed in the sense of Hadamard. Moreover, we investigate the problem taking into account the disturbance both vari...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2021-09, Vol.44 (5), p.3345-3359
Main Authors: Dien, Nguyen Minh, Trong, Dang Duc
Format: Article
Language:English
Subjects:
Applications of Mathematics
Diffusion
Diffusion coefficient
Exact solutions
Mathematics
Mathematics and Statistics
Regularization
Regularization methods
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Summary:This paper investigates the nonlinear backward fractional diffusion equations (BFDEs) having a variable order and variable diffusion coefficient. It is well-known that the BFDEs are ill-posed in the sense of Hadamard. Moreover, we investigate the problem taking into account the disturbance both variable diffusion coefficient and variable order. This may lead to some common regularization strategy to failure. Therefore, we propose a regularization method for this kind of problem. Under some appropriate regularity assumptions of the exact solution, a convergence estimate of Holder-type is proved.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-021-01113-y