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2022 On the Reconstruction of Convection Coefficient in a Semilinear Anomalous Diffusion System
Liangliang Sun, Maoli Chang
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Taiwanese J. Math. Advance Publication 1-25 (2022). DOI: 10.11650/tjm/220301

Abstract

In the paper, we study an inverse problem of recovering a time-dependent convection coefficient from the measured data at an interior/boundary point in a one-dimensional nonlinear subdiffusion model with non-homogeneous boundary conditions. Due to the nonlinearity and non-homogeneous boundary conditions of the system, such an inverse problem is novel and important. We first investigate the unique existence and some regularities of the solution to forward problem by using the transposition method and the fixed point theorem. Then a conditional stability of the inverse problem is obtained based on the regularity of solution for the direct problem and some generalized Gronwall's inequalities. Finally, we transform the inverse problem into a variational problem. The existence and convergence of the regularization solution for the variational problem are proved and we use a modified Levenberg–Marquardt method to find an approximate convection coefficient function. The efficiency and accuracy of the algorithm are illustrated with two numerical examples.

Funding Statement

This work is supported by the Youth Science and Technology Fund of Gansu Province (no. 20JR10RA099), the Innovation Capacity Improvement Project for Colleges and Universities of Gansu Province (no. 2020B-088), the Young Teachers' Scientific Research Ability Promotion Project of NWNU (no. NWNU-LKQN-18-31) and the Doctoral Scientific Research Foundation of NWNU (no. 6014/0002020204).

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Liangliang Sun. Maoli Chang. "On the Reconstruction of Convection Coefficient in a Semilinear Anomalous Diffusion System." Taiwanese J. Math. Advance Publication 1 - 25, 2022. https://doi.org/10.11650/tjm/220301

Information

Published: 2022
First available in Project Euclid: 21 March 2022

Digital Object Identifier: 10.11650/tjm/220301

Subjects:
Primary: 35R25 , 35R30 , 65M30

Keywords: identification of convection coefficient , modified Levenberg–Marquardt algorithm , non-homogeneous boundary conditions , semilinear fractional diffusion equation , stability

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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