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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
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 
We give a complete description of the longtime asymptotic profile of the solution to a free boundary model considered recently in [
References:
[1] 
S. B. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math., 390 (1988), 7996. doi: 10.1515/crll.1988.390.79. 
[2] 
H. Berestycki, O. Diekmann, C. J. Nagelkerke, P. A. Zegeling, Can a species keep pace with a shifting climate?, Bull. Math. Biol., 71 (2009), 399429. doi: 10.1007/s1153800893675. 
[3] 
J. Cai, B. Lou, M. Zhou, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations, 26 (2014), 10071028. doi: 10.1007/s108840149404z. 
[4] 
E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations McGrawHill, New York, 1955. 
[5] 
Y. Du, Z. Lin, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377405. doi: 10.1137/090771089. 
[6] 
Y. Du, B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc. (JEMS), 17 (2015), 26732724. doi: 10.4171/JEMS/568. 
[7] 
Y. Du, B. Lou, M. Zhou, Nonlinear diffusion problems with free boundaries: Convergence, transition speed and zero number arguments, SIAM J. Math. Anal., 47 (2015), 35553584. doi: 10.1137/140994848. 
[8] 
Y. Du, L. Ma, Logistic type equations on $\mathbb{R}^N$ by a squeezing method involving boundary blowup solutions, J. London Math. Soc., 64 (2001), 107124. doi: 10.1017/S0024610701002289. 
[9] 
Y. Du, H. Matsuzawa, M. Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal., 46 (2014), 375396. doi: 10.1137/130908063. 
[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, Semiwave and spreading speed for the diffusive competition model with a free boundary J. Math. Pures Appl. , in press. 
[12] 
H. Gu, B. Lou, M. Zhou, Long time behavior of solutions of FisherKPP equation with advection and free boundaries, J. Funct. Anal., 269 (2015), 17141768. doi: 10.1016/j.jfa.2015.07.002. 
[13] 
Y. Kaneko, H. Matsuzawa, Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advectiondiffusion equations, J. Math. Anal. Appl., 428 (2015), 4376. doi: 10.1016/j.jmaa.2015.02.051. 
[14] 
B. Li, S. Bewick, J. Shang, W. Fagan, Persistence and spread of a species with a shifting habitat edge, SIAM J. Appl. Math., 74 (2014), 13971417. doi: 10.1137/130938463. 
show all references
References:
[1] 
S. B. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math., 390 (1988), 7996. doi: 10.1515/crll.1988.390.79. 
[2] 
H. Berestycki, O. Diekmann, C. J. Nagelkerke, P. A. Zegeling, Can a species keep pace with a shifting climate?, Bull. Math. Biol., 71 (2009), 399429. doi: 10.1007/s1153800893675. 
[3] 
J. Cai, B. Lou, M. Zhou, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations, 26 (2014), 10071028. doi: 10.1007/s108840149404z. 
[4] 
E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations McGrawHill, New York, 1955. 
[5] 
Y. Du, Z. Lin, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377405. doi: 10.1137/090771089. 
[6] 
Y. Du, B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc. (JEMS), 17 (2015), 26732724. doi: 10.4171/JEMS/568. 
[7] 
Y. Du, B. Lou, M. Zhou, Nonlinear diffusion problems with free boundaries: Convergence, transition speed and zero number arguments, SIAM J. Math. Anal., 47 (2015), 35553584. doi: 10.1137/140994848. 
[8] 
Y. Du, L. Ma, Logistic type equations on $\mathbb{R}^N$ by a squeezing method involving boundary blowup solutions, J. London Math. Soc., 64 (2001), 107124. doi: 10.1017/S0024610701002289. 
[9] 
Y. Du, H. Matsuzawa, M. Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal., 46 (2014), 375396. doi: 10.1137/130908063. 
[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, Semiwave and spreading speed for the diffusive competition model with a free boundary J. Math. Pures Appl. , in press. 
[12] 
H. Gu, B. Lou, M. Zhou, Long time behavior of solutions of FisherKPP equation with advection and free boundaries, J. Funct. Anal., 269 (2015), 17141768. doi: 10.1016/j.jfa.2015.07.002. 
[13] 
Y. Kaneko, H. Matsuzawa, Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advectiondiffusion equations, J. Math. Anal. Appl., 428 (2015), 4376. doi: 10.1016/j.jmaa.2015.02.051. 
[14] 
B. Li, S. Bewick, J. Shang, W. Fagan, Persistence and spread of a species with a shifting habitat edge, SIAM J. Appl. Math., 74 (2014), 13971417. doi: 10.1137/130938463. 
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