Stability of solutions of a class of nonlinear fractional diffusion equations with respect to a pseudo‐differential operator

In this paper, we study the forward and the backward in time problems for a class of nonlinear diffusion equations with respect to the pseudo‐differential operator. Herein, we investigate the stability of the solution of the forward problem in relationship with parameters of the pseudo‐differential...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2019-05, Vol.42 (8), p.2513-2532
Main Authors: Nguyen Minh, Dien, Dang Duc, Trong
Format: Article
Language:English
Subjects:
backward problem
Differential equations
Forward problem
fractional derivatives
ill‐posed problem
Mathematical analysis
Nonlinear equations
Operators (mathematics)
Parameters
pseudo‐differential
Stability
well‐posed problem
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Summary:In this paper, we study the forward and the backward in time problems for a class of nonlinear diffusion equations with respect to the pseudo‐differential operator. Herein, we investigate the stability of the solution of the forward problem in relationship with parameters of the pseudo‐differential operator and initial data. Besides, as known, the backward in time problem is instability. Hence, we give a method to regularize the solution of the backward problem in the case of the parameters are perturbed.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5528