On inverse source term for heat equation with memory term-Reference-Cited by-同舟云学术

On inverse source term for heat equation with memory term

Published:2024-01-01 Issue:1 Volume:57 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Duc Nam Bui¹,Hai Nguyen Minh²,Hoan Luu Vu Cam³,Long Le Dinh⁴

Affiliation:

1. Ho Chi Minh City University of Industry and Trade , Ho Chi Minh City , Vietnam

2. Department of Mathematical Economics, Banking University of Ho Chi Minh City , Ho Chi Minh City , Vietnam

3. Faculty of Basic Science, Posts and Telecommunications Institute of Technology , Ho Chi Minh City , Vietnam

4. Falculty of Maths, FPT University HCM, Saigon Hi-tech Park , Ho Chi Minh City , Vietnam

Abstract

Abstract In this article, we first study the inverse source problem for parabolic with memory term. We show that our problem is ill-posed in the sense of Hadamard. Then, we construct the convergence result when the parameter tends to zero. We also investigate the regularized solution using the Fourier truncation method. The error estimate between the regularized solution and the exact solution is obtained.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/dema-2023-0138/pdf

Reference34 articles.

1. Y. Yamada, Asymptotic stability for some systems of semilinear Volterra diffusion equations, J. Differential Equations 52 (1984), no. 3, 295–326, DOI: https://doi.org/10.1016/0022-0396(84)90165-7.

2. S. A. Gourley and N. F. Britton, A predator-prey reaction-diffusion system with nonlocal effects, J. Math. Biol. 34 (1996), no. 3, 297–333.

3. Q. Tao and H. Gao, On the null controllability of heat equation with memory, J. Math. Anal. Appl. 440 (2016), no. 1, 1–13, DOI: https://doi.org/10.1016/j.jmaa.2016.03.036.

4. E. G. Savateev, On problems of determining the source function in a parabolic equation, J. Inverse Ill-Posed Probl. 3 (1995), no. 1, 83–102.

5. D. D. Trong, N. T. Long, and A. P. N. Dinh, Nonhomogeneous heat equation: Identification and regularization for the inhomogeneous term, J. Math. Anal. Appl. 312 (2005), no. 1, 93–104, DOI: https://doi.org/10.1515/jiip.1995.3.1.83.