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Spreading Speeds of Time-Dependent Partially Degenerate Reaction-Diffusion Systems

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Abstract

This paper is concerned with the spreading speeds of time dependent partially degenerate reaction-diffusion systems with monostable nonlinearity. By using the principal Lyapunov exponent theory, the author first proves the existence, uniqueness and stability of spatially homogeneous entire positive solution for time dependent partially degenerate reaction-diffusion system. Then the author shows that such system has a finite spreading speed interval in any direction and there is a spreading speed for the partially degenerate system under certain conditions. The author also applies these results to a time dependent partially degenerate epidemic model.

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Acknowledgement

The author would like to thank the referee for valuable comments and suggestions which improved the presentation of this manuscript.

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Authors and Affiliations

  1. School of Science, Chang’an University, Xi’an, 710064, China

    Jia Liu

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  1. Jia Liu
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Correspondence to Jia Liu.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 41801029, 11701041) and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2020JM-223).

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Liu, J. Spreading Speeds of Time-Dependent Partially Degenerate Reaction-Diffusion Systems. Chin. Ann. Math. Ser. B 43, 79–94 (2022). https://doi.org/10.1007/s11401-022-0306-9

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  • DOI: https://doi.org/10.1007/s11401-022-0306-9

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