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Preface
Spreading speed revisited: Analysis of a free boundary model
1. | School of Science and Technology, University of New England, Armidale, NSW 2351, Australia, Australia, Australia |
References:
[1] |
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in "Partial Differential Equations and Related Topics" Lecture Notes in Math., 446, Springer, Berlin, (1975), 5-49. |
[2] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 30 (1978), 33-76.
doi: 10.1016/0001-8708(78)90130-5. |
[3] |
H. Berestycki, F. Hamel and H. Matano, Bistable traveling waves around an obstacle, Comm. Pure Appl. Math., 62 (2009), 729-788.
doi: 10.1002/cpa.20275. |
[4] |
H. Berestycki, F. Hamel and G. Nadin, Asymptotic spreading in heterogeneous diffusive excitable media, J. Funct. Anal., 255 (2008), 2146-2189.
doi: 10.1016/j.jfa.2008.06.030. |
[5] |
H. Berestycki, F. Hamel and N. Nadirashvili, The speed of propagation for KPP type problems. I. Periodic framework, J. Eur. Math. Soc., 7 (2005), 173-213.
doi: 10.4171/JEMS/26. |
[6] |
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. |
[7] |
Y. Du, "Order Structure and Topological Methods in Nonlinear Partial Differential Equations," 1, Maximum Principles and Applications, World Scientific, Singapore, 2006.
doi: 10.1142/9789812774446. |
[8] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, II, J. Diff. Eqns., 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[9] |
Y. Du and Z. M. Guo, The Stefan problem for the Fisher-KPP equation, J. Diff. Eqns., 253 (2012), 996-1035.
doi: 10.1016/j.jde.2012.04.014. |
[10] |
Y. Du, Z. M. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment, preprint, 2011. |
[11] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 1305-1333.
doi: 10.1137/090771089. |
[12] |
Y. Du and B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, preprint, 2011. |
[13] |
Y. Du and H. Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, J. European Math. Soc., 12 (2010), 279-312.
doi: 10.4171/JEMS/198. |
[14] |
X. Fauvergue, J-C. Malausa, L. Giuge and F. Courchamp, Invading parasitoids suffer no Allee effect: A manipulative field experiment, Ecology, 88 (2008), 2392-2403. |
[15] |
I. Filin, R. D. Holt and M. Barfield, The relation of density regulation to habitat specialization, evolution of a speciesrange, and the dynamics of biological invasions, Am. Nat., 172 (2008), 233-247. |
[16] |
R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), 335-369. |
[17] |
K. P. Hadeler and F. Rothe, Travelling fronts in nonlinear diffusion equations, J. Math. Biol., 2 (1975), 251-263. |
[18] |
D. Hilhorst, M. Iida, M. Mimura and H. Ninomiya, A competition-diffusion system approximation to the classical two-phase Stefan problem, Japan J. Indust. Appl. Math., 18 (2001), 161-180.
doi: 10.1007/BF03168569. |
[19] |
A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Ètude de l'équation de la diffusion avec croissance de la quantitéde matière et son application à un problème biologique, Bull. Univ. Moscou Sér. Internat. A1 (1937), 1-26; English transl. in: "Dynamics of Curved Fronts" (ed. P. Pelcé), Academic Press, (1988), 105-130. |
[20] |
A. M. Kramer, B. Dennis, A. M. Liebhold and J. M. Drake, The evidence for Allee effects, Popul. Ecol., 51 (2009), 341-354. |
[21] |
M. A. Lewis and P. Kareiva, Allee dynamics and the spreading of invasive organisms, Theor. Population Bio., 43 (1993), 141-158. |
[22] |
X. Liang and X-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[23] |
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. |
[24] |
J. L. Lockwood, M. F. Hoopes and M. P. Marchetti, "Invasion Ecology," Blackwell Publishing, 2007. |
[25] |
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. |
[26] |
R. Peng and X. Q. Zhao, The diffusive logistic model with a free boundary and seasonal succession, Discrete Cont. Dyn. Syst. A., to appear. |
[27] |
L. I. Rubinstein, "The Stefan Problem," Amer. Math. Soc., Providence, RI, 1971. |
[28] |
N. Shigesada and K. Kawasaki, "Biological Invasions: Theory and Practice," Oxford Series in Ecology and Evolution, Oxford Univ. Press., Oxford, 1997. |
[29] |
J. G. Skellam, Random dispersal in theoretical populations, Biometrika, 38 (1951), 196-218. |
[30] |
H. F. Weinberger, On spreading speeds and traveling waves for growth and migration models in a periodic habitat, J. Math. Biol., 45 (2002), 511-548.
doi: 10.1007/s00285-002-0169-3. |
[31] |
H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.
doi: 10.1007/s00285-007-0078-6. |
[32] |
J. X. Xin, Front propagation in heterogeneous media, SIAM Rev., 42 (2000), 161-230.
doi: 10.1137/S0036144599364296. |
show all references
References:
[1] |
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in "Partial Differential Equations and Related Topics" Lecture Notes in Math., 446, Springer, Berlin, (1975), 5-49. |
[2] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 30 (1978), 33-76.
doi: 10.1016/0001-8708(78)90130-5. |
[3] |
H. Berestycki, F. Hamel and H. Matano, Bistable traveling waves around an obstacle, Comm. Pure Appl. Math., 62 (2009), 729-788.
doi: 10.1002/cpa.20275. |
[4] |
H. Berestycki, F. Hamel and G. Nadin, Asymptotic spreading in heterogeneous diffusive excitable media, J. Funct. Anal., 255 (2008), 2146-2189.
doi: 10.1016/j.jfa.2008.06.030. |
[5] |
H. Berestycki, F. Hamel and N. Nadirashvili, The speed of propagation for KPP type problems. I. Periodic framework, J. Eur. Math. Soc., 7 (2005), 173-213.
doi: 10.4171/JEMS/26. |
[6] |
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. |
[7] |
Y. Du, "Order Structure and Topological Methods in Nonlinear Partial Differential Equations," 1, Maximum Principles and Applications, World Scientific, Singapore, 2006.
doi: 10.1142/9789812774446. |
[8] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, II, J. Diff. Eqns., 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[9] |
Y. Du and Z. M. Guo, The Stefan problem for the Fisher-KPP equation, J. Diff. Eqns., 253 (2012), 996-1035.
doi: 10.1016/j.jde.2012.04.014. |
[10] |
Y. Du, Z. M. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment, preprint, 2011. |
[11] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 1305-1333.
doi: 10.1137/090771089. |
[12] |
Y. Du and B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, preprint, 2011. |
[13] |
Y. Du and H. Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, J. European Math. Soc., 12 (2010), 279-312.
doi: 10.4171/JEMS/198. |
[14] |
X. Fauvergue, J-C. Malausa, L. Giuge and F. Courchamp, Invading parasitoids suffer no Allee effect: A manipulative field experiment, Ecology, 88 (2008), 2392-2403. |
[15] |
I. Filin, R. D. Holt and M. Barfield, The relation of density regulation to habitat specialization, evolution of a speciesrange, and the dynamics of biological invasions, Am. Nat., 172 (2008), 233-247. |
[16] |
R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), 335-369. |
[17] |
K. P. Hadeler and F. Rothe, Travelling fronts in nonlinear diffusion equations, J. Math. Biol., 2 (1975), 251-263. |
[18] |
D. Hilhorst, M. Iida, M. Mimura and H. Ninomiya, A competition-diffusion system approximation to the classical two-phase Stefan problem, Japan J. Indust. Appl. Math., 18 (2001), 161-180.
doi: 10.1007/BF03168569. |
[19] |
A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Ètude de l'équation de la diffusion avec croissance de la quantitéde matière et son application à un problème biologique, Bull. Univ. Moscou Sér. Internat. A1 (1937), 1-26; English transl. in: "Dynamics of Curved Fronts" (ed. P. Pelcé), Academic Press, (1988), 105-130. |
[20] |
A. M. Kramer, B. Dennis, A. M. Liebhold and J. M. Drake, The evidence for Allee effects, Popul. Ecol., 51 (2009), 341-354. |
[21] |
M. A. Lewis and P. Kareiva, Allee dynamics and the spreading of invasive organisms, Theor. Population Bio., 43 (1993), 141-158. |
[22] |
X. Liang and X-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[23] |
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. |
[24] |
J. L. Lockwood, M. F. Hoopes and M. P. Marchetti, "Invasion Ecology," Blackwell Publishing, 2007. |
[25] |
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. |
[26] |
R. Peng and X. Q. Zhao, The diffusive logistic model with a free boundary and seasonal succession, Discrete Cont. Dyn. Syst. A., to appear. |
[27] |
L. I. Rubinstein, "The Stefan Problem," Amer. Math. Soc., Providence, RI, 1971. |
[28] |
N. Shigesada and K. Kawasaki, "Biological Invasions: Theory and Practice," Oxford Series in Ecology and Evolution, Oxford Univ. Press., Oxford, 1997. |
[29] |
J. G. Skellam, Random dispersal in theoretical populations, Biometrika, 38 (1951), 196-218. |
[30] |
H. F. Weinberger, On spreading speeds and traveling waves for growth and migration models in a periodic habitat, J. Math. Biol., 45 (2002), 511-548.
doi: 10.1007/s00285-002-0169-3. |
[31] |
H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.
doi: 10.1007/s00285-007-0078-6. |
[32] |
J. X. Xin, Front propagation in heterogeneous media, SIAM Rev., 42 (2000), 161-230.
doi: 10.1137/S0036144599364296. |
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