An inverse problem for nonlocal reaction-diffusion equations with time-delay

Abstract

The reaction-diffusion equations have been studied in various aspects of nature, such as heat transfer and biological dynamic modelling. In this paper, we study a nonlocal reaction-diffusion model with time delay associated with the density and diffusion behaviour of biological populations. Based on our previous conclusions and numerical strategy of the direct problem, we continue to study the inverse problem about the diffusion coefficient as well as the parameters in the birth function, and also perform numerical simulations with error analysis. In addition, we further generalize the constant diffusion coefficient to the position-dependent diffusion rate, which is intended to improve the generalizability to multiple organisms diffusion in nature.

Keywords:

• Reaction-Diffusion equations
• inverse problem
• diffusion rate
• identification algorithm

AMS Subject Classifications:

• 35R30
• 65M32

Acknowledgements

We would like to express our sincere appreciation to Prof. Ming Mei, McGill University, Canada. His guidance and previous research provide us with new ideas and academic support during the first-named author's academic stay at MU.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 https://www.ncbi.nlm.nih.gov/

Additional information

Funding

Supported by the National Natural Scientific Foundation of China [grant numbers: 12371428 and 11871435], the Fundamental Research Funds for the Chinese Central Universities, SUFE and the China Scholarship Council (No. 202106480020).