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

Chengxia Lei; Yihong Du

doi:10.3934/dcdsb.2017045

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2017, Volume 22, Issue 3: 895-911. Doi: 10.3934/dcdsb.2017045

This issue Previous Article Global existence and regularity results for strongly coupled nonregular parabolic systems via iterative methods Next Article Transboundary capital and pollution flows and the emergence of regional inequalities

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

Chengxia Lei^1, and
Yihong Du^2,

1.
Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
2.
School of Science and Technology, University of New England, Armidale, NSW 2351, Australia

Received: August 31, 2015

Revised: October 31, 2015

Published: September 2017

C. Lei is supported by the China Scholarship Council for 2 years of study at University of New England, Y. Du was supported by the Australian Research Council.

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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.

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Mathematics Subject Classification: Primary:35K20, 35R35;Secondary:92B05.

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References

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