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On the dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response
The infected frontier in an SEIR epidemic model with infinite delay
1. | School of Mathematical Science, Yangzhou University, Yangzhou 225002, China |
2. | Department of Mathematics, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240 |
References:
[1] |
L. Caffarelli and S. Salsa, "A Geometric Approach to Free Boundary Problems," American Mathematical Society, 68 2005. |
[2] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[3] |
J. Crank, "Free and Moving Boundary Problems," Clarendon Press, Oxford 1984. |
[4] |
Y. H. Du and Z. M. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, J. Differential Equations, 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[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 and Z. G. Lin, The diffusive competition model with a free boundary: invasion of a superior or inferior competitor, Discrete Contin. Dyn. Syst. Ser. B, preprint, arXiv:1303.0454. |
[7] |
M. Fila and P. Souplet, Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem, Interfaces Free Bound., 3 (2001), 337-344. |
[8] |
G. Röst and J. H. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 5 (2008), 389-402.
doi: 10.3934/mbe.2008.5.389. |
[9] |
H. Ghidouche, P. Souplet and D. Tarzia, Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary, Proc. Amer. Math. Soc., 129 (2001), 781-792.
doi: 10.1090/S0002-9939-00-05705-1. |
[10] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, third ed., 840, Springer-Verlag, Berlin, New York 1981. |
[11] |
D. Hilhorst, M. Mimura and R. Schätzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Anal. Real World Appl., 4 (2003), 261-285.
doi: 10.1016/S1468-1218(02)00009-3. |
[12] |
K. I. Kim, Z. G. Lin and Z. Ling, Global existence and blowup of solutions to a free boundary problem for mutualistic model, Sci. China Math., 53 (2010), 2085-2095.
doi: 10.1007/s11425-010-4007-6. |
[13] |
O. A. Ladyženskaja, V. A. Solonnikov, N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc, Providence, RI, 1968. |
[14] |
Z. G. Lin, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), 1883-1892.
doi: 10.1088/0951-7715/20/8/004. |
[15] |
Z. G. Lin and M. Pedersen, Stability in a diffusive food-chain model with Michaelis-Menten functional response, Nonlinear Anal., 57 (2004), 421-433.
doi: 10.1016/j.na.2004.02.022. |
[16] |
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. |
[17] |
M. Mimura, Y. Yamada and S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), 477-498. |
[18] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations, Hiroshima Math. J., 17 (1987), 241-280. |
[19] |
L. I. Rubinstein, "The Stefan Problem," American Mathematical Society, Providence, RI 1971. |
show all references
References:
[1] |
L. Caffarelli and S. Salsa, "A Geometric Approach to Free Boundary Problems," American Mathematical Society, 68 2005. |
[2] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[3] |
J. Crank, "Free and Moving Boundary Problems," Clarendon Press, Oxford 1984. |
[4] |
Y. H. Du and Z. M. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, J. Differential Equations, 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[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 and Z. G. Lin, The diffusive competition model with a free boundary: invasion of a superior or inferior competitor, Discrete Contin. Dyn. Syst. Ser. B, preprint, arXiv:1303.0454. |
[7] |
M. Fila and P. Souplet, Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem, Interfaces Free Bound., 3 (2001), 337-344. |
[8] |
G. Röst and J. H. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 5 (2008), 389-402.
doi: 10.3934/mbe.2008.5.389. |
[9] |
H. Ghidouche, P. Souplet and D. Tarzia, Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary, Proc. Amer. Math. Soc., 129 (2001), 781-792.
doi: 10.1090/S0002-9939-00-05705-1. |
[10] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, third ed., 840, Springer-Verlag, Berlin, New York 1981. |
[11] |
D. Hilhorst, M. Mimura and R. Schätzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Anal. Real World Appl., 4 (2003), 261-285.
doi: 10.1016/S1468-1218(02)00009-3. |
[12] |
K. I. Kim, Z. G. Lin and Z. Ling, Global existence and blowup of solutions to a free boundary problem for mutualistic model, Sci. China Math., 53 (2010), 2085-2095.
doi: 10.1007/s11425-010-4007-6. |
[13] |
O. A. Ladyženskaja, V. A. Solonnikov, N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc, Providence, RI, 1968. |
[14] |
Z. G. Lin, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), 1883-1892.
doi: 10.1088/0951-7715/20/8/004. |
[15] |
Z. G. Lin and M. Pedersen, Stability in a diffusive food-chain model with Michaelis-Menten functional response, Nonlinear Anal., 57 (2004), 421-433.
doi: 10.1016/j.na.2004.02.022. |
[16] |
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. |
[17] |
M. Mimura, Y. Yamada and S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), 477-498. |
[18] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations, Hiroshima Math. J., 17 (1987), 241-280. |
[19] |
L. I. Rubinstein, "The Stefan Problem," American Mathematical Society, Providence, RI 1971. |
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