Global dynamics for a class of reaction–diffusion equations with distributed delay and non-monotone bistable nonlinearity

ABSTRACT

This work is devoted to the study of the global dynamics for a class of reaction–diffusion equations with distributed delay and non-monotone bistable nonlinearity. By using a comparison result, we characterize the basins of attraction of each steady state, that is, the trivial one and two positive steady states. We apply our results to a diffusive blowflies model with Allee effect and distributed delay.

KEYWORDS:

• Reaction–diffusion equations
• distributed delay
• bistable nonlinearity
• global dynamics

AMS SUBJECT CLASSIFICATIONS:

• 35R10
• 35B40
• 35Q92

Acknowledgments

The authors would like to thank the associate editor and anonymous reviewers for their helpful comments to the earlier version of this manuscript.

Disclosure statement

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

Additional information

Funding

The first author is partially supported by the JSPS Grant-in-Aid for Early-Career Scientists [No.19K14594] and the Japan Agency for Medical Research Development [No. JP20fk0108535]. The second author is supported by DGRSDT, Algeria, project PRFU, code C00L03UN130120200004.