Abstract
This paper is concerned with the asymptotic profiles of positive solutions for diffusive logistic equations. The aim is to study the sharp effect of nonlinear diffusion functions. Both the classical reaction–diffusion equation and nonlocal dispersal equation are investigated. We prove the sharp change occurs in reaction–diffusion equation by regularity estimates and compact principle. Due to lack of compactness and regularities theory for nonlocal problems, we obtain the sharp changes by nonlocal estimates and comparison arguments. Our result reveals the nonlinear term plays quite different roles between evolution problem and stationary solution problem.
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Acknowledgements
The author would like to thank the anonymous reviewer for his/her helpful comments. This work was partially supported by National Natural Foundation of China (11731005), Fundamental Research Funds for the Central Universities (lzujbky-2021-52) and China postdoctoral Science Foundation (2017M611084).
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Sun, JW. Asymptotic profiles in diffusive logistic equations. Z. Angew. Math. Phys. 72, 152 (2021). https://doi.org/10.1007/s00033-021-01582-y
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DOI: https://doi.org/10.1007/s00033-021-01582-y