Work

A Regularization Method for Backward Problems of Singularly Perturbed Parabolic and Fractional Diffusion Equations

Year: 2025

Type: article

Abstract: In this paper, backward problems of singularly perturbed parabolic and fractional diffusion equations are studied from the additional temperature data at fixed time $ t=T$. We analyze the ill-posedness of these two inverse problems, and apply the quasi-reversibility regularization method to solve these problems. Then we obtain the convergence rates of logarithmic and Hölder types for the backward problems. Finally, several one- and two-dimensional numerical examples are given to verify the effectiveness and feasibility of the proposed method.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240424

Authors: Jin Wen, Yun-Long Liu, Xue-Juan Ren, Donal O'Regan

Institutions: Northwest Normal University, Tarim University, Ollscoil na Gaillimhe – University of Galway

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411533658

FWCI: 1.7

Cites:

Cited by: 1

Related to: 10