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Different asymptotic spreading speeds induced by advection in a diffusion problem with free boundaries


Authors: Hong Gu, Zhigui Lin and Bendong Lou
Journal: Proc. Amer. Math. Soc. 143 (2015), 1109-1117
MSC (2010): Primary 35B40, 35K57, 34C37, 92B05
Published electronically: November 5, 2014
MathSciNet review: 3293726
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Abstract: In this paper, we consider a Fisher-KPP equation with an advection term and two free boundaries, which models the behavior of an invasive species in one dimension space. When spreading happens (that is, the solution converges to a positive constant), we use phase plane analysis and upper/lower solutions to prove that the rightward and leftward asymptotic spreading speeds exist and both are positive constants. Moreover, one of them is bigger and the other is smaller than the spreading speed in the corresponding problem without advection term.


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Additional Information

Hong Gu
Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
Email: honggu87@126.com

Zhigui Lin
Affiliation: School of Mathematical Science, Yangzhou University, Yangzhou 225002, People’s Republic of China
Email: zglin68@hotmail.com

Bendong Lou
Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
Email: blou@tongji.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2014-12214-3
Received by editor(s): January 13, 2013
Received by editor(s) in revised form: March 27, 2013
Published electronically: November 5, 2014
Additional Notes: This paper was partly supported by the NSFC (11271285, 11071209).
Communicated by: Yingfei Yi
Article copyright: © Copyright 2014 American Mathematical Society