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On existence of wavefront solutions in mixed monotone reaction-diffusion systems
A revisit to the diffusive logistic model with free boundary condition
1. | School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China |
2. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7 |
References:
[1] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Netw. Heterog. Media., 7 (2012), 583-603.
doi: 10.3934/nhm.2012.7.583. |
[2] |
R. S. Cantrell and C. Cosner, Diffusive logistic equations with indefinite weights: Population models in a disrupted environments, Proc. Roy. Soc. Edinburgh., 112 (1989), 293-318.
doi: 10.1017/S030821050001876X. |
[3] |
R. S. Cantrell, C. Cosner and V. Hutson, Ecological models, permanence and spatial heterogeneity, Rocky Mount. J. Math., 26 (1996), 1-35.
doi: 10.1216/rmjm/1181072101. |
[4] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[5] |
S. B. Cui, Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors, J. Funct. Anal., 245 (2007), 1-18.
doi: 10.1016/j.jfa.2006.12.020. |
[6] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, Journal of Differential Equations, 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[7] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[8] |
Y. Du and B. D. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17 (2015), 2673-2724, arXiv:1301.5373
doi: 10.4171/JEMS/568. |
[9] |
Y. Du, H. Matsuzawa and M. L. 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. |
[10] |
Y. Du, H. Matsuzawa and M. L. Zhou, Spreading speed and profile for nonlinear Stefan problems in high space dimensions, J. Math. Pures Appl., 103 (2015), 741-787.
doi: 10.1137/130908063. |
[11] |
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. |
[12] |
H. Ghidouche, P. Souplet and D. Tarzia, Decay of global solutions, stability and blow-up for a reaction-diffusion problem with free boundary, Proc. Am. Math. Soc., 129 (2001), 781-792.
doi: 10.1090/S0002-9939-00-05705-1. |
[13] |
K. I. Kim, Z. G. Lin and Q. Y. Zhang, An SIR epidemic model with free boundary, Nonlinear Analysis: Real World Applications., 14 (2013), 1992-2001.
doi: 10.1016/j.nonrwa.2013.02.003. |
[14] |
C. X. Lei, K. Kim and Z. G. Lin, The spreading frontiers of avian-human influenza described by the free boundary, Sci. China Math., 57 (2014), 971-990.
doi: 10.1007/s11425-013-4652-7. |
[15] |
C. X. Lei, Z. G. Lin and Q. Y. Zhang, The spreading front of invasive species in favorable habitat or unfavorable habitat, J. Differential Equations., 257 (2014), 145-166.
doi: 10.1016/j.jde.2014.03.015. |
[16] |
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. |
[17] |
Z. G. Lin, Y. N. Zhao and P. Zhou, The infected frontier in an SEIR epidemic model with infinite delay, Discrete. Contin. Dyn. Syst. Ser. B, 18 (2013), 2355-2376.
doi: 10.3934/dcdsb.2013.18.2355. |
[18] |
L. I. Rubinstein, The Stefan Problem, American Mathematical Society, Providence, RI 1971. |
[19] |
F. E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology, 44 (1963), 651-663.
doi: 10.2307/1933011. |
[20] |
P. Zhou, J. Bao and Z. G. Lin, Global existence and blowup of a localized problem with free boundary, Nonlinear Anal., 74 (2011), 2523-2533.
doi: 10.1016/j.na.2010.11.047. |
[21] |
P. Zhou and Z. G. Lin, Global existence and blowup of a nonlocal problem in space with free boundary, J. Funct. Anal., 262 (2012), 3409-3429.
doi: 10.1016/j.jfa.2012.01.018. |
[22] |
P. Zhou and Z. G. Lin, Global fast and slow solutions of a localized problem with free boundary, Sci. China Math., 55 (2012), 1937-1950.
doi: 10.1007/s11425-012-4443-6. |
[23] |
P. Zhou and D. M. Xiao, The diffusive logistic model with a free boundary in heterogeneous environment, J. Differential Equations., 256 (2014), 1927-1954.
doi: 10.1016/j.jde.2013.12.008. |
show all references
References:
[1] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Netw. Heterog. Media., 7 (2012), 583-603.
doi: 10.3934/nhm.2012.7.583. |
[2] |
R. S. Cantrell and C. Cosner, Diffusive logistic equations with indefinite weights: Population models in a disrupted environments, Proc. Roy. Soc. Edinburgh., 112 (1989), 293-318.
doi: 10.1017/S030821050001876X. |
[3] |
R. S. Cantrell, C. Cosner and V. Hutson, Ecological models, permanence and spatial heterogeneity, Rocky Mount. J. Math., 26 (1996), 1-35.
doi: 10.1216/rmjm/1181072101. |
[4] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[5] |
S. B. Cui, Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors, J. Funct. Anal., 245 (2007), 1-18.
doi: 10.1016/j.jfa.2006.12.020. |
[6] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, Journal of Differential Equations, 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[7] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[8] |
Y. Du and B. D. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17 (2015), 2673-2724, arXiv:1301.5373
doi: 10.4171/JEMS/568. |
[9] |
Y. Du, H. Matsuzawa and M. L. 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. |
[10] |
Y. Du, H. Matsuzawa and M. L. Zhou, Spreading speed and profile for nonlinear Stefan problems in high space dimensions, J. Math. Pures Appl., 103 (2015), 741-787.
doi: 10.1137/130908063. |
[11] |
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. |
[12] |
H. Ghidouche, P. Souplet and D. Tarzia, Decay of global solutions, stability and blow-up for a reaction-diffusion problem with free boundary, Proc. Am. Math. Soc., 129 (2001), 781-792.
doi: 10.1090/S0002-9939-00-05705-1. |
[13] |
K. I. Kim, Z. G. Lin and Q. Y. Zhang, An SIR epidemic model with free boundary, Nonlinear Analysis: Real World Applications., 14 (2013), 1992-2001.
doi: 10.1016/j.nonrwa.2013.02.003. |
[14] |
C. X. Lei, K. Kim and Z. G. Lin, The spreading frontiers of avian-human influenza described by the free boundary, Sci. China Math., 57 (2014), 971-990.
doi: 10.1007/s11425-013-4652-7. |
[15] |
C. X. Lei, Z. G. Lin and Q. Y. Zhang, The spreading front of invasive species in favorable habitat or unfavorable habitat, J. Differential Equations., 257 (2014), 145-166.
doi: 10.1016/j.jde.2014.03.015. |
[16] |
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. |
[17] |
Z. G. Lin, Y. N. Zhao and P. Zhou, The infected frontier in an SEIR epidemic model with infinite delay, Discrete. Contin. Dyn. Syst. Ser. B, 18 (2013), 2355-2376.
doi: 10.3934/dcdsb.2013.18.2355. |
[18] |
L. I. Rubinstein, The Stefan Problem, American Mathematical Society, Providence, RI 1971. |
[19] |
F. E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology, 44 (1963), 651-663.
doi: 10.2307/1933011. |
[20] |
P. Zhou, J. Bao and Z. G. Lin, Global existence and blowup of a localized problem with free boundary, Nonlinear Anal., 74 (2011), 2523-2533.
doi: 10.1016/j.na.2010.11.047. |
[21] |
P. Zhou and Z. G. Lin, Global existence and blowup of a nonlocal problem in space with free boundary, J. Funct. Anal., 262 (2012), 3409-3429.
doi: 10.1016/j.jfa.2012.01.018. |
[22] |
P. Zhou and Z. G. Lin, Global fast and slow solutions of a localized problem with free boundary, Sci. China Math., 55 (2012), 1937-1950.
doi: 10.1007/s11425-012-4443-6. |
[23] |
P. Zhou and D. M. Xiao, The diffusive logistic model with a free boundary in heterogeneous environment, J. Differential Equations., 256 (2014), 1927-1954.
doi: 10.1016/j.jde.2013.12.008. |
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