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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.
doi: 10.1137/S0036141099351693. |
[3] |
J. Crank, "Free and Moving Boundary Problems,", Clarendon Press, (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.
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.
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, (). Google Scholar |
[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.
|
[8] |
G. Röst and J. H. Wu, SEIR epidemiological model with varying infectivity and infinite delay,, Math. Biosci. Eng., 5 (2008), 389.
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.
doi: 10.1090/S0002-9939-00-05705-1. |
[10] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,", Lecture Notes in Mathematics, 840 (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.
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.
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, (1968).
|
[14] |
Z. G. Lin, A free boundary problem for a predator-prey model,, Nonlinearity, 20 (2007), 1883.
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.
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.
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.
|
[18] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations,, Hiroshima Math. J., 17 (1987), 241.
|
[19] |
L. I. Rubinstein, "The Stefan Problem,", American Mathematical Society, (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.
doi: 10.1137/S0036141099351693. |
[3] |
J. Crank, "Free and Moving Boundary Problems,", Clarendon Press, (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.
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.
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, (). Google Scholar |
[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.
|
[8] |
G. Röst and J. H. Wu, SEIR epidemiological model with varying infectivity and infinite delay,, Math. Biosci. Eng., 5 (2008), 389.
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.
doi: 10.1090/S0002-9939-00-05705-1. |
[10] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,", Lecture Notes in Mathematics, 840 (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.
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.
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, (1968).
|
[14] |
Z. G. Lin, A free boundary problem for a predator-prey model,, Nonlinearity, 20 (2007), 1883.
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.
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.
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.
|
[18] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations,, Hiroshima Math. J., 17 (1987), 241.
|
[19] |
L. I. Rubinstein, "The Stefan Problem,", American Mathematical Society, (1971).
|
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