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Entire solution of the degenerate Fisher equation

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Abstract

This paper deals with the solutions defined for all time of the degenerate Fisher equation. Some solutions are obtained by considering two traveling fronts with critical speed that come from both sides of the X-axis and mix. Unfortunately, the entire solutions which behave as two opposite wave fronts with non-critical speed approaching each other from both sides of the X-axis can not be obtained, because the essential difficulty originates from the algebraic decay rate of the fronts with non-critical speed.

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Acknowledgements

The author is very grateful to professor Yaping Wu, professor Jongshenq Guo and professor Xing Liang for valuable discussions.

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Authors and Affiliations

  1. School of Science, Beijing Technology and Business University, Beijing, 100048, China

    Li-na Wang

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  1. Li-na Wang
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Correspondence to Li-na Wang.

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Supported by the National Natural Science Foundation of China (Nos. 11501016, 11471221), Beijing Municipal Education Commission (KZ201310028030) and Research Foundation for Youth Scholars of Beijing Technology and Business University (QNJJ2015-16).

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Wang, Ln. Entire solution of the degenerate Fisher equation. Acta Math. Appl. Sin. Engl. Ser. 33, 75–82 (2017). https://doi.org/10.1007/s10255-017-0638-5

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  • DOI: https://doi.org/10.1007/s10255-017-0638-5

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