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Axisymmetry of locally bounded solutions to an Euler-Lagrange system of the weighted Hardy-Littlewood-Sobolev inequality
The diffusive logistic model with a free boundary and seasonal succession
1. | Department of Mathematics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, China, and Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada |
2. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7 |
References:
[1] |
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation,, in, 446 (1975), 5.
|
[2] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics,, Adv. Math., 30 (1978), 33.
doi: 10.1016/0001-8708(78)90130-5. |
[3] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model,, Networks and Heterogeneous Media, (). Google Scholar |
[4] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing,, SIAM J. Math. Anal., 32 (2000), 778.
doi: 10.1137/S0036141099351693. |
[5] |
D. L. DeAngelis, J. C. Trexler and D. D. Donalson, "Competition Dynamics in a Seasionally Varying Wetland,", Chapter 1, (2009), 1.
|
[6] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II,, J. Differential Equations, 250 (2011), 4336.
doi: 10.1016/j.jde.2011.02.011. |
[7] |
Y. Du, Z. M. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment,, preprint, (2011). Google Scholar |
[8] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary,, SIAM J. Math. Anal., 42 (2010), 377.
doi: 10.1137/090771089. |
[9] |
P. J. DuBowy, Waterfowl communities and seasonal environments: Temporal variabolity in interspecific competition,, Ecology, 69 (1988), 1439. Google Scholar |
[10] |
S.-B. Hsu and X.-Q. Zhao, A Lotka-Volterra competition model with seasonal succession,, J. Math. Biol., 64 (2012), 109.
doi: 10.1007/s00285-011-0408-6. |
[11] |
S. S. Hu and A. J. Tessier, Seasonal succession and the strength of intra- and interspecific competition in a Daphnia assemblage,, Ecology, 76 (1995), 2278. Google Scholar |
[12] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,", Amer. Math. Soc. Providence, (1968).
|
[13] |
X. Liang, Y. Yi and X.-Q. Zhao, Spreading speeds and traveling waves for periodic evolution systems,, J. Differential Equations, 231 (2006), 57.
doi: 10.1016/j.jde.2006.04.010. |
[14] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications,, Comm. Pure Appl. Math., 60 (2007), 1.
doi: 10.1002/cpa.20154. |
[15] |
Z. G. Lin, A free boundary problem for a predator-prey model,, Nonlinearity, 20 (2007), 1883.
doi: 10.1088/0951-7715/20/8/004. |
[16] |
E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light,, American Naturalist, 157 (2001), 170. Google Scholar |
[17] |
T. R. Malthus, "An Essay on the Principle of Population,", 1798. Printed for J. Johnson in St. Pauls Church-Yard, (1998). Google Scholar |
[18] |
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology,, Japan J. Appl. Math., 2 (1985), 151.
doi: 10.1007/BF03167042. |
[19] |
G. Nadin, The principal eigenvalue of a space-time periodic parabolic operator,, Ann. Mat. Pura Appl., 188 (2009), 269.
doi: 10.1007/s10231-008-0075-4. |
[20] |
R. Peng and D. Wei, The periodic-parabolic logistic equation on $\R^N$,, Discrete and Continuous Dyn. Syst. Series A, 32 (2012), 619.
|
[21] |
H. F. Weinberger, Long-time behavior of a class of biological models,, SIAM J. Math. Anal., 13 (1982), 353.
doi: 10.1137/0513028. |
[22] |
X.-Q. Zhao, "Dynamical Systems in Population Biology,", Springer-Verlag, (2003).
|
show all references
References:
[1] |
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation,, in, 446 (1975), 5.
|
[2] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics,, Adv. Math., 30 (1978), 33.
doi: 10.1016/0001-8708(78)90130-5. |
[3] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model,, Networks and Heterogeneous Media, (). Google Scholar |
[4] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing,, SIAM J. Math. Anal., 32 (2000), 778.
doi: 10.1137/S0036141099351693. |
[5] |
D. L. DeAngelis, J. C. Trexler and D. D. Donalson, "Competition Dynamics in a Seasionally Varying Wetland,", Chapter 1, (2009), 1.
|
[6] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II,, J. Differential Equations, 250 (2011), 4336.
doi: 10.1016/j.jde.2011.02.011. |
[7] |
Y. Du, Z. M. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment,, preprint, (2011). Google Scholar |
[8] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary,, SIAM J. Math. Anal., 42 (2010), 377.
doi: 10.1137/090771089. |
[9] |
P. J. DuBowy, Waterfowl communities and seasonal environments: Temporal variabolity in interspecific competition,, Ecology, 69 (1988), 1439. Google Scholar |
[10] |
S.-B. Hsu and X.-Q. Zhao, A Lotka-Volterra competition model with seasonal succession,, J. Math. Biol., 64 (2012), 109.
doi: 10.1007/s00285-011-0408-6. |
[11] |
S. S. Hu and A. J. Tessier, Seasonal succession and the strength of intra- and interspecific competition in a Daphnia assemblage,, Ecology, 76 (1995), 2278. Google Scholar |
[12] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,", Amer. Math. Soc. Providence, (1968).
|
[13] |
X. Liang, Y. Yi and X.-Q. Zhao, Spreading speeds and traveling waves for periodic evolution systems,, J. Differential Equations, 231 (2006), 57.
doi: 10.1016/j.jde.2006.04.010. |
[14] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications,, Comm. Pure Appl. Math., 60 (2007), 1.
doi: 10.1002/cpa.20154. |
[15] |
Z. G. Lin, A free boundary problem for a predator-prey model,, Nonlinearity, 20 (2007), 1883.
doi: 10.1088/0951-7715/20/8/004. |
[16] |
E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light,, American Naturalist, 157 (2001), 170. Google Scholar |
[17] |
T. R. Malthus, "An Essay on the Principle of Population,", 1798. Printed for J. Johnson in St. Pauls Church-Yard, (1998). Google Scholar |
[18] |
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology,, Japan J. Appl. Math., 2 (1985), 151.
doi: 10.1007/BF03167042. |
[19] |
G. Nadin, The principal eigenvalue of a space-time periodic parabolic operator,, Ann. Mat. Pura Appl., 188 (2009), 269.
doi: 10.1007/s10231-008-0075-4. |
[20] |
R. Peng and D. Wei, The periodic-parabolic logistic equation on $\R^N$,, Discrete and Continuous Dyn. Syst. Series A, 32 (2012), 619.
|
[21] |
H. F. Weinberger, Long-time behavior of a class of biological models,, SIAM J. Math. Anal., 13 (1982), 353.
doi: 10.1137/0513028. |
[22] |
X.-Q. Zhao, "Dynamical Systems in Population Biology,", Springer-Verlag, (2003).
|
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