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, Issue 3, May 2017

doi:10.3934/dcdsb.2017045      Abstract        References        Full text (380.0K)           Related Articles

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)

1 S. B. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math., 390 (1988), 79-96.       
2 H. Berestycki, O. Diekmann, C. J. Nagelkerke and P. A. Zegeling, Can a species keep pace with a shifting climate?, Bull. Math. Biol., 71 (2009), 399-429.       
3 J. Cai, B. Lou and M. Zhou, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations, 26 (2014), 1007-1028.       
4 E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.       
5 Y. Du and Z. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.       
6 Y. Du and B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc. (JEMS), 17 (2015), 2673-2724.       
7 Y. Du, B. Lou and M. Zhou, Nonlinear diffusion problems with free boundaries: Convergence, transition speed and zero number arguments, SIAM J. Math. Anal., 47 (2015), 3555-3584.       
8 Y. Du and L. Ma, Logistic type equations on $\mathbbR^N$ by a squeezing method involving boundary blow-up solutions, J. London Math. Soc., 64 (2001), 107-124.       
9 Y. Du, H. Matsuzawa and M. Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal., 46 (2014), 375-396.       
10 Y. Du, L. Wei and L. Zhou, Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary, Preprint, arXiv:1508.06246
11 Y. Du, M. Wang and M. Zhou, Semi-wave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pures Appl.,
12 H. Gu, B. Lou and M. Zhou, Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries, J. Funct. Anal., 269 (2015), 1714-1768.       
13 Y. Kaneko and H. Matsuzawa, Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations, J. Math. Anal. Appl., 428 (2015), 43-76.       
14 B. Li, S. Bewick, J. Shang and W. Fagan, Persistence and spread of a species with a shifting habitat edge, SIAM J. Appl. Math., 74 (2014), 1397-1417.       

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