Uniqueness result for an age-dependent reaction–diffusion problem

Abstract

This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction–diffusion problem when the source term depends on the density, indicating the presence of, for example, mortality and reaction processes. Our result shows that in a spatial environment, if two population densities obey the same evolution equation and possess the same terminal data of time and age, then their distributions must coincide therein.

COMMUNICATED BY:

• D. N. Hao

Keywords:

• Backward age-dependent reaction–diffusion
• uniqueness
• population dynamics

2000 Mathematics Subject Classifications:

• 35A07
• 35K57
• 92D25
• 45Q05

Acknowledgements

This work is in commemoration of the first death anniversary of V. A. K's father. V. A. K thanks Prof. Nguyen Huy Tuan for introducing him the ultraparabolic problem. The work of V.A.K. was supported by the Research Foundation-Flanders (FWO) under the project ‘Approximations for forward and inverse reaction-diffusion problems related to cancer models’.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Vo Anh Khoa  http://orcid.org/0000-0003-4233-0895