Electron. J. Differential Equations, Vol. 2018 (2018), No. 185, pp. 1-12.

Spreading solutions for a reaction diffusion equation with free boundaries in time-periodic environment

Fang Li, Junfan Lu

In this article, we consider a reaction diffusion equation with free boundaries in a time-periodic environment. Such models can be used to describe the spreading of a new or invasive species over a one-dimensional habitat, with the free boundaries representing the expanding fronts. We study an equation with a general time-periodic nonlinearity, and present some sufficient conditions for spreading phenomena. We also use time-periodic semi-waves to characterize the spreading solutions.

Submitted December 20, 2017. Published November 15, 2018.
Math Subject Classifications: 35B40, 35R35, 35K55, 92B05.
Key Words: Spreading phenomenon; free boundary; time-periodic environment.

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Fang Li
Mathematics and Science College
Shanghai Normal University
Shanghai 200234, China
email: lifwx@shnu.edu.cn
Junfan Lu
School of Mathematical Sciences
Tongji University
Shanghai 200092, China
email: 1410541@tongji.edu.cn

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