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Isolated singularity for semilinear elliptic equations
Asymptotic behavior of solutions for competitive models with a free boundary
1. | Department of Mathematics, Tongji University, Shanghai, 200092 |
References:
[1] |
S. B. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math., 390 (1988), 79-96.
doi: 10.1515/crll.1988.390.79. |
[2] |
J. J. Cai, B. D. Lou and M. L. Zhou, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations, 26 (2014), 1007-1028.
doi: 10.1007/s10884-014-9404-z. |
[3] |
C. H. Chang and C. C. Chen, Travelling wave solutions of a free boundary problem for a two-species competitive model, Commun. Pure Appl. Anal., 12 (2013), 1065-1074.
doi: 10.3934/cpaa.2013.12.1065. |
[4] |
X. F. Chen, B. D. Lou, M. L. Zhou and T. Giletti, Long time behavior of solutions of a reaction-diffusion equation on unbounded intervals with Robin boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press, 2014.
doi: 10.1016/j.anihpc.2014.08.004. |
[5] |
Y. H. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[6] |
Y. H. Du, H. Matsuzawa and M. L. Zhou, Spreading speed determined by nonlinear free boundary problems in high dimensions, J. Math. Pures Appl., preprint. |
[7] |
P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361. |
[8] |
O. A. Ladyzenskaya, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Academic Press, New York, London, 1968. |
[9] |
G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996.
doi: 10.1142/3302. |
[10] |
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math., 2 (1985), 151-186.
doi: 10.1007/BF03167042. |
[11] |
M. Mimura, Y. Yamada and S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), 477-498. |
[12] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations, Hiroshima Math. J., 17 (1987), 241-280. |
[13] |
J. Yang and B. D. Lou, Traveling wave solutions of competitive models with free boundaries, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 817-826.
doi: 10.3934/dcdsb.2014.19.817. |
show all references
References:
[1] |
S. B. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math., 390 (1988), 79-96.
doi: 10.1515/crll.1988.390.79. |
[2] |
J. J. Cai, B. D. Lou and M. L. Zhou, Asymptotic behavior of solutions of a reaction diffusion equation with free boundary conditions, J. Dynam. Differential Equations, 26 (2014), 1007-1028.
doi: 10.1007/s10884-014-9404-z. |
[3] |
C. H. Chang and C. C. Chen, Travelling wave solutions of a free boundary problem for a two-species competitive model, Commun. Pure Appl. Anal., 12 (2013), 1065-1074.
doi: 10.3934/cpaa.2013.12.1065. |
[4] |
X. F. Chen, B. D. Lou, M. L. Zhou and T. Giletti, Long time behavior of solutions of a reaction-diffusion equation on unbounded intervals with Robin boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press, 2014.
doi: 10.1016/j.anihpc.2014.08.004. |
[5] |
Y. H. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[6] |
Y. H. Du, H. Matsuzawa and M. L. Zhou, Spreading speed determined by nonlinear free boundary problems in high dimensions, J. Math. Pures Appl., preprint. |
[7] |
P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361. |
[8] |
O. A. Ladyzenskaya, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Academic Press, New York, London, 1968. |
[9] |
G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996.
doi: 10.1142/3302. |
[10] |
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math., 2 (1985), 151-186.
doi: 10.1007/BF03167042. |
[11] |
M. Mimura, Y. Yamada and S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), 477-498. |
[12] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations, Hiroshima Math. J., 17 (1987), 241-280. |
[13] |
J. Yang and B. D. Lou, Traveling wave solutions of competitive models with free boundaries, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 817-826.
doi: 10.3934/dcdsb.2014.19.817. |
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