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Periodic solutions of some classes of continuous second-order differential equations
Expanding speed of the habitat for a species in an advective environment
1. | School of Mathematical Sciences, Tongji University, Shanghai 200092, China |
2. | School of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing 210023, China |
3. | Mathematics & Science College, Shanghai Normal University, Shanghai 200234, China |
Recently, Gu et al. [
References:
[1] |
I. E. Averill,
The Effect of Intermediate Advection on Two Competing Species Doctor of Philosophy, Ohio State University, Mathematics, 2012. |
[2] |
Y. Du and Z. G. Lin,
Spreading-vanishing dichtomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 45 (2013), 1995-1996.
doi: 10.1137/090771089. |
[3] |
Y. Du and B. Lou,
Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17 (2015), 2673-2724.
doi: 10.4171/JEMS/568. |
[4] |
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.
doi: 10.1137/130908063. |
[5] |
J. Ge, K. I. Kim, Z. G. Lin and H. Zhu,
A SIS reaction-diffusion-advection model in a low-risk and high-risk domain, J. Differential Equations, 259 (2015), 5486-5509.
doi: 10.1016/j.jde.2015.06.035. |
[6] |
H. Gu, Z. Lin and B. Lou,
Long time behavior of solutions of a diffusion-advection logistic model with free boundaries, Appl. Math. Lett., 37 (2014), 49-53.
doi: 10.1016/j.aml.2014.05.015. |
[7] |
H. Gu, Z. Lin and B. Lou,
Different asymptotic spreading speeds induced by advection in a diffusion problem with free boundaries, Proc. Amer. Math. Soc., 143 (2015), 1109-1117.
doi: 10.1090/S0002-9939-2014-12214-3. |
[8] |
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.
doi: 10.1016/j.jfa.2015.07.002. |
[9] |
N. A. Maidana and H. Yang,
Spatial spreading of West Nile virus described by traveling waves, J. Theoret. Biol., 258 (2009), 403-417.
doi: 10.1016/j.jtbi.2008.12.032. |
[10] |
Y. Zhao and M. Wang, A reaction-diffusion-advection equation with mixed and free boundary conditions, preprint, arXiv: 1312.7751. |
show all references
References:
[1] |
I. E. Averill,
The Effect of Intermediate Advection on Two Competing Species Doctor of Philosophy, Ohio State University, Mathematics, 2012. |
[2] |
Y. Du and Z. G. Lin,
Spreading-vanishing dichtomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 45 (2013), 1995-1996.
doi: 10.1137/090771089. |
[3] |
Y. Du and B. Lou,
Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17 (2015), 2673-2724.
doi: 10.4171/JEMS/568. |
[4] |
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.
doi: 10.1137/130908063. |
[5] |
J. Ge, K. I. Kim, Z. G. Lin and H. Zhu,
A SIS reaction-diffusion-advection model in a low-risk and high-risk domain, J. Differential Equations, 259 (2015), 5486-5509.
doi: 10.1016/j.jde.2015.06.035. |
[6] |
H. Gu, Z. Lin and B. Lou,
Long time behavior of solutions of a diffusion-advection logistic model with free boundaries, Appl. Math. Lett., 37 (2014), 49-53.
doi: 10.1016/j.aml.2014.05.015. |
[7] |
H. Gu, Z. Lin and B. Lou,
Different asymptotic spreading speeds induced by advection in a diffusion problem with free boundaries, Proc. Amer. Math. Soc., 143 (2015), 1109-1117.
doi: 10.1090/S0002-9939-2014-12214-3. |
[8] |
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.
doi: 10.1016/j.jfa.2015.07.002. |
[9] |
N. A. Maidana and H. Yang,
Spatial spreading of West Nile virus described by traveling waves, J. Theoret. Biol., 258 (2009), 403-417.
doi: 10.1016/j.jtbi.2008.12.032. |
[10] |
Y. Zhao and M. Wang, A reaction-diffusion-advection equation with mixed and free boundary conditions, preprint, arXiv: 1312.7751. |
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