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Winter 2020 Regularization of a terminal value nonlinear diffusion equation with conformable time derivative
Vo Van Au, Yong Zhou, Nguyen Huu Can, Nguyen Tuy Tuan
J. Integral Equations Applications 32(4): 397-416 (Winter 2020). DOI: 10.1216/jie.2020.32.397

Abstract

For an inverse nonlinear diffusion equation with conformable time derivative, we study the ill-posed property in the sense of Hadamard. To obtain a stable numerical solution, we propose two regularization methods. The results of existence and uniqueness, regularity and stability of the regularized problem are obtained. We also show that the corresponding regularized solutions converge to the sought solution strongly in L2(d) uniformly under some a priori assumptions on the solution.

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Vo Van Au. Yong Zhou. Nguyen Huu Can. Nguyen Tuy Tuan. "Regularization of a terminal value nonlinear diffusion equation with conformable time derivative." J. Integral Equations Applications 32 (4) 397 - 416, Winter 2020. https://doi.org/10.1216/jie.2020.32.397

Information

Received: 10 July 2019; Revised: 17 January 2020; Accepted: 20 January 2020; Published: Winter 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/jie.2020.32.397

Subjects:
Primary: 26A33, 35B65, 35R11

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.32 • No. 4 • Winter 2020
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