Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model

Pages: 895 - 911, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017045

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Chengxia Lei - Department of Mathematics, University of Science and Technology of China, Hefei 230026, China (email)
Yihong Du - School of Science and Technology, University of New England, Armidale, NSW 2351, Australia (email)

Abstract: We give a complete description of the long-time asymptotic profile of the solution to a free boundary model considered recently in [10]. This model describes the spreading of an invasive species in an environment which shifts with a constant speed, and the research of [10] indicates that the species may vanish, or spread successfully, or fall in a borderline case. In the case of successful spreading, the long-time behavior of the population is not completely understood in [10]. Here we show that the spreading of the species is governed by two traveling waves, one has the speed of the shifting environment, giving the profile of the retreating tail of the population, while the other has a faster speed determined by a semi-wave, representing the profile of the advancing front of the population.

Keywords:  Shifting climate, free boundary, traveling wave.
Mathematics Subject Classification:  Primary: 35K20, 35R35; Secondary: 92B05.

Received: September 2015;      Revised: November 2015;      Available Online: January 2017.