메뉴 건너뛰기




Volumn 72, Issue 5, 2010, Pages 1166-1191

Spreading Speeds in Slowly Oscillating Environments

Author keywords

Allee effect; Fragmentation; Periodic environment; Reaction diffusion; Spreading speeds

Indexed keywords


EID: 77149153766     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-009-9486-7     Document Type: Article
Times cited : (30)

References (55)
  • 2
    • 0002488752 scopus 로고
    • Nonlinear diffusion in population genetics, combustion and nerve propagation
    • Lectures Notes Math, New York: Springer
    • Aronson, D. G., Weinberger, H. G., 1975. Nonlinear diffusion in population genetics, combustion and nerve propagation. In: Partial Differential Equations and Related Topics, Lectures Notes Math., vol. 446, pp. 5-49. Springer, New York.
    • (1975) Partial Differential Equations and Related Topics , vol.446 , pp. 5-49
    • Aronson, D.G.1    Weinberger, H.G.2
  • 3
    • 54049103533 scopus 로고    scopus 로고
    • Dynamique en temps grand pour une classe d'équations de type KPP en milieu périodique
    • Bages, M., Martinez, P., Roquejoffre, J.-M., 2008. Dynamique en temps grand pour une classe d'équations de type KPP en milieu périodique. C. R. Acad. Sci. Ser. I Math. 346, 1051-1056.
    • (2008) C. R. Acad. Sci. Ser. I Math. , vol.346 , pp. 1051-1056
    • Bages, M.1    Martinez, P.2    Roquejoffre, J.-M.3
  • 4
    • 33947307582 scopus 로고    scopus 로고
    • Multiple Allee effects and population management
    • Berec, L., Angulo, E., Courchamp, F., 2007. Multiple Allee effects and population management. Trends Ecol. Evol. 22, 185-191.
    • (2007) Trends Ecol. Evol. , vol.22 , pp. 185-191
    • Berec, L.1    Angulo, E.2    Courchamp, F.3
  • 5
    • 0036298883 scopus 로고    scopus 로고
    • Front propagation in periodic excitable media
    • Berestycki, H., Hamel, F., 2002. Front propagation in periodic excitable media. Commun. Pure Appl. Math. 55(8), 949-1032.
    • (2002) Commun. Pure Appl. Math. , vol.55 , Issue.8 , pp. 949-1032
    • Berestycki, H.1    Hamel, F.2
  • 6
    • 11944266033 scopus 로고    scopus 로고
    • The principal eigenvalue of elliptic operators with large drift and applications to nonlinear propagation phenomena
    • Berestycki, H., Hamel, F., Nadirashvili, N., 2005a. The principal eigenvalue of elliptic operators with large drift and applications to nonlinear propagation phenomena. Commun. Math. Phys. 253(2), 451-480.
    • (2005) Commun. Math. Phys. , vol.253 , Issue.2 , pp. 451-480
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 7
    • 16644384785 scopus 로고    scopus 로고
    • The speed of propagation for KPP type problems. I: Periodic framework
    • Berestycki, H., Hamel, F., Nadirashvili, N., 2005b. The speed of propagation for KPP type problems. I: Periodic framework. J. Eur. Math. Soc. 7(2), 173-213.
    • (2005) J. Eur. Math. Soc. , vol.7 , Issue.2 , pp. 173-213
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 8
    • 22244440170 scopus 로고    scopus 로고
    • Analysis of the periodically fragmented environment model: I-Species persistence
    • Berestycki, H., Hamel, F., Roques, L., 2005c. Analysis of the periodically fragmented environment model: I-Species persistence. J. Math. Biol. 51(1), 75-113.
    • (2005) J. Math. Biol. , vol.51 , Issue.1 , pp. 75-113
    • Berestycki, H.1    Hamel, F.2    Roques, L.3
  • 9
    • 16644386250 scopus 로고    scopus 로고
    • Analysis of the periodically fragmented environment model: II-Biological invasions and pulsating travelling fronts
    • Berestycki, H., Hamel, F., Roques, L., 2005d. Analysis of the periodically fragmented environment model: II-Biological invasions and pulsating travelling fronts. J. Math. Pures Appl. 84(8), 1101-1146.
    • (2005) J. Math. Pures Appl. , vol.84 , Issue.8 , pp. 1101-1146
    • Berestycki, H.1    Hamel, F.2    Roques, L.3
  • 10
    • 58049150839 scopus 로고    scopus 로고
    • Asymptotic spreading in heterogeneous diffusive excitable media
    • Berestycki, H., Hamel, F., Nadin, G., 2008. Asymptotic spreading in heterogeneous diffusive excitable media. J. Funct. Anal. 255(9), 2146-2189.
    • (2008) J. Funct. Anal. , vol.255 , Issue.9 , pp. 2146-2189
    • Berestycki, H.1    Hamel, F.2    Nadin, G.3
  • 11
    • 0003175686 scopus 로고
    • Convergence of solutions of the Kolmogorov equation to travelling waves
    • Bramson, M., 1983. Convergence of solutions of the Kolmogorov equation to travelling waves. Mem. Am. Math. Soc. 44.
    • (1983) Mem. Am. Math. Soc , pp. 44
    • Bramson, M.1
  • 13
    • 0000604313 scopus 로고
    • Allee effects: Population growth, critical density, and the chance of extinction
    • Dennis, B., 1989. Allee effects: population growth, critical density, and the chance of extinction. Nat. Res. Model. 3, 481-538.
    • (1989) Nat. Res. Model. , vol.3 , pp. 481-538
    • Dennis, B.1
  • 14
    • 45749147424 scopus 로고    scopus 로고
    • Pulsating travelling fronts: Asymptotics and homogenization regimes
    • El Smaily, M., 2008. Pulsating travelling fronts: asymptotics and homogenization regimes. Eur. J. Appl. Math. 19(4), 393-434.
    • (2008) Eur. J. Appl. Math. , vol.19 , Issue.4 , pp. 393-434
    • El Smaily, M.1
  • 15
    • 70349865019 scopus 로고    scopus 로고
    • Homogenization and influence of fragmentation in a biological invasion model
    • El Smaily, M., Hamel, F., Roques, L., 2009. Homogenization and influence of fragmentation in a biological invasion model. Discrete Contin. Dyn. Syst., Ser. A 25, 321-342.
    • (2009) Discrete Contin. Dyn. Syst., Ser. A , vol.25 , pp. 321-342
    • El Smaily, M.1    Hamel, F.2    Roques, L.3
  • 16
    • 0002910353 scopus 로고
    • Long-time behavior of solutions of bistable non-linear diffusion equations
    • Fife, P. C., 1979. Long-time behavior of solutions of bistable non-linear diffusion equations. Arch. Ration. Mech. Anal. 70(1), 31-46.
    • (1979) Arch. Ration. Mech. Anal. , vol.70 , Issue.1 , pp. 31-46
    • Fife, P.C.1
  • 17
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • Fisher, R. A., 1937. The wave of advance of advantageous genes. Ann. Eugen. 7, 335-369.
    • (1937) Ann. Eugen. , vol.7 , pp. 335-369
    • Fisher, R.A.1
  • 18
    • 0040731158 scopus 로고
    • Limit-theorems for large deviations and reaction-diffusion equations
    • Freidlin, M., 1985. Limit-theorems for large deviations and reaction-diffusion equations. Ann. Probab. 13(3), 639-675.
    • (1985) Ann. Probab. , vol.13 , Issue.3 , pp. 639-675
    • Freidlin, M.1
  • 19
    • 0008835676 scopus 로고
    • On the propagation of concentration waves in periodic and random media
    • Freidlin, M., Gärtner, J., 1979. On the propagation of concentration waves in periodic and random media. Sov. Math. Dokl. 20, 1282-1286.
    • (1979) Sov. Math. Dokl. , vol.20 , pp. 1282-1286
    • Freidlin, M.1    Gärtner, J.2
  • 20
    • 0031748982 scopus 로고    scopus 로고
    • Allee effects limit population viability of an annual plant
    • Groom, M. J., 1998. Allee effects limit population viability of an annual plant. Am. Nat. 151(6), 487-496.
    • (1998) Am. Nat. , vol.151 , Issue.6 , pp. 487-496
    • Groom, M.J.1
  • 22
    • 41149173181 scopus 로고    scopus 로고
    • Qualitative properties of monostable pulsating fronts: Exponential decay and monotonicity
    • Hamel, F., 2008. Qualitative properties of monostable pulsating fronts: exponential decay and monotonicity. J. Math. Pures Appl. 89, 355-399.
    • (2008) J. Math. Pures Appl. , vol.89 , pp. 355-399
    • Hamel, F.1
  • 23
    • 78751477218 scopus 로고    scopus 로고
    • Uniqueness and stability properties of monostable pulsating fronts
    • (to appear)
    • Hamel, F., Roques, L., 2010. Uniqueness and stability properties of monostable pulsating fronts. J. Eur. Math. Soc. (to appear).
    • (2010) J. Eur. Math. Soc
    • Hamel, F.1    Roques, L.2
  • 26
    • 0021085261 scopus 로고
    • Analyzing insect movement as a correlated random-walk
    • Kareiva, P. M., Shigesada, N., 1983. Analyzing insect movement as a correlated random-walk. Oecologia 56(2-3), 234-238.
    • (1983) Oecologia , vol.56 , Issue.2-3 , pp. 234-238
    • Kareiva, P.M.1    Shigesada, N.2
  • 28
    • 34248182000 scopus 로고    scopus 로고
    • An integrodifference model for biological invasions in a periodically fragmented environment
    • Kawasaki, K., Shigesada, N., 2007. An integrodifference model for biological invasions in a periodically fragmented environment. Jpn. J. Ind. Appl. Math. 24(1), 3-15.
    • (2007) Jpn. J. Ind. Appl. Math. , vol.24 , Issue.1 , pp. 3-15
    • Kawasaki, K.1    Shigesada, N.2
  • 29
    • 0346338087 scopus 로고    scopus 로고
    • Modeling biological invasions into periodically fragmented environments
    • Kinezaki, N., Kawasaki, K., Takasu, F., Shigesada, N., 2003. Modeling biological invasions into periodically fragmented environments. Theor. Popul. Biol. 64(3), 291-302.
    • (2003) Theor. Popul. Biol. , vol.64 , Issue.3 , pp. 291-302
    • Kinezaki, N.1    Kawasaki, K.2    Takasu, F.3    Shigesada, N.4
  • 30
    • 34248191611 scopus 로고    scopus 로고
    • Spatial dynamics of invasion in sinusoidally varying environments
    • Kinezaki, N., Kawasaki, K., Shigesada, N., 2006. Spatial dynamics of invasion in sinusoidally varying environments. Popul. Ecol. 48(4), 263-270.
    • (2006) Popul. Ecol. , vol.48 , Issue.4 , pp. 263-270
    • Kinezaki, N.1    Kawasaki, K.2    Shigesada, N.3
  • 31
    • 0002722044 scopus 로고
    • Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique
    • Kolmogorov, A. N., Petrovsky, I. G., Piskunov, N. S., 1937. Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bull. Univ. État Mosc., Sér. Int. A 1, 1-26.
    • (1937) Bull. Univ. État Mosc., Sér. Int. A , vol.1 , pp. 1-26
    • Kolmogorov, A.N.1    Petrovsky, I.G.2    Piskunov, N.S.3
  • 32
    • 77954620658 scopus 로고    scopus 로고
    • A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction-diffusion equations
    • (to appear)
    • Liang, X., Lin, X., Matano, H., 2010. A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction-diffusion equations. Trans. Am. Math. Soc. (to appear).
    • (2010) Trans. Am. Math. Soc
    • Liang, X.1    Lin, X.2    Matano, H.3
  • 33
    • 0023707009 scopus 로고
    • The form and consequences of random-walk movement models
    • Marsh, L. M., Jones, R. E., 1988. The form and consequences of random-walk movement models. J. Theor. Biol. 133(1), 113-131.
    • (1988) J. Theor. Biol. , vol.133 , Issue.1 , pp. 113-131
    • Marsh, L.M.1    Jones, R.E.2
  • 34
    • 0030727039 scopus 로고    scopus 로고
    • The Allee effect, finding mates and theoretical models
    • McCarthy, M. A., 1997. The Allee effect, finding mates and theoretical models. Ecol. Model. 103(1), 99-102.
    • (1997) Ecol. Model. , vol.103 , Issue.1 , pp. 99-102
    • McCarthy, M.A.1
  • 35
    • 0026360188 scopus 로고
    • Dependence of epidemic and population velocities on basic parameters
    • Mollison, D., 1991. Dependence of epidemic and population velocities on basic parameters. Math. Biosci. 107, 255-287.
    • (1991) Math. Biosci. , vol.107 , pp. 255-287
    • Mollison, D.1
  • 36
    • 68849091810 scopus 로고    scopus 로고
    • Travelling fronts in space-time periodic media
    • Nadin, G., 2009. Travelling fronts in space-time periodic media. J. Math. Pures Appl. 92, 232-262.
    • (2009) J. Math. Pures Appl. , vol.92 , pp. 232-262
    • Nadin, G.1
  • 37
    • 77950794741 scopus 로고    scopus 로고
    • The effect of the Schwarz rearrangement on the periodic principal eigenvalue of a nonsymmetric operator
    • (to appear)
    • Nadin, G., 2010. The effect of the Schwarz rearrangement on the periodic principal eigenvalue of a nonsymmetric operator. SIAM J. Math. Anal. (to appear).
    • (2010) SIAM J. Math. Anal
    • Nadin, G.1
  • 38
    • 28444472406 scopus 로고    scopus 로고
    • Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle
    • Nolen, J., Xin, J., 2005. Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle. Discrete Contin. Dyn. Syst., Ser. A 13, 1217-1234.
    • (2005) Discrete Contin. Dyn. Syst., Ser. A , vol.13 , pp. 1217-1234
    • Nolen, J.1    Xin, J.2
  • 39
    • 33845907733 scopus 로고    scopus 로고
    • Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds
    • Nolen, J., Rudd, M., Xin, J., 2005. Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds. Theor. Popul. Biol. 2, 1-24.
    • (2005) Theor. Popul. Biol. , vol.2 , pp. 1-24
    • Nolen, J.1    Rudd, M.2    Xin, J.3
  • 41
    • 35248856029 scopus 로고    scopus 로고
    • Mathematical analysis of the optimal habitat configurations for species persistence
    • Roques, L., Hamel, F., 2007. Mathematical analysis of the optimal habitat configurations for species persistence. Math. Biosci. 210(1), 34-59.
    • (2007) Math. Biosci. , vol.210 , Issue.1 , pp. 34-59
    • Roques, L.1    Hamel, F.2
  • 42
    • 41049100658 scopus 로고    scopus 로고
    • A population facing climate change: Joint influences of Allee effects and environmental boundary geometry
    • Roques, L., Roques, A., Berestycki, H., Kretzschmar, A., 2008. A population facing climate change: joint influences of Allee effects and environmental boundary geometry. Popul. Ecol. 50(2), 215-225.
    • (2008) Popul. Ecol. , vol.50 , Issue.2 , pp. 215-225
    • Roques, L.1    Roques, A.2    Berestycki, H.3    Kretzschmar, A.4
  • 43
    • 35348956875 scopus 로고    scopus 로고
    • KPP pulsating front speed-up by flows
    • Ryzhik, L., Zlatos, A., 2007. KPP pulsating front speed-up by flows. Commun. Math. Sci. 5, 575-593.
    • (2007) Commun. Math. Sci. , vol.5 , pp. 575-593
    • Ryzhik, L.1    Zlatos, A.2
  • 45
    • 33645087891 scopus 로고
    • Traveling periodic-waves in heterogeneous environments
    • Shigesada, N., Kawasaki, K., Teramoto, E., 1986. Traveling periodic-waves in heterogeneous environments. Theor. Popul. Biol. 30(1), 143-160.
    • (1986) Theor. Popul. Biol. , vol.30 , Issue.1 , pp. 143-160
    • Shigesada, N.1    Kawasaki, K.2    Teramoto, E.3
  • 46
    • 0017172820 scopus 로고
    • On two types of moving front in quasilinear diffusion
    • Stokes, A. N., 1976. On two types of moving front in quasilinear diffusion. Math. Biosci. 31, 307-315.
    • (1976) Math. Biosci. , vol.31 , pp. 307-315
    • Stokes, A.N.1
  • 49
    • 0142119503 scopus 로고    scopus 로고
    • Front propagation into unstable states
    • van Saarloos, W., 2003. Front propagation into unstable states. Phys. Rep. 386, 29-222.
    • (2003) Phys. Rep. , vol.386 , pp. 29-222
    • van Saarloos, W.1
  • 51
    • 0029662720 scopus 로고    scopus 로고
    • Dispersal, population growth, and the Allee effect: Dynamics of the house finch invasion of eastern North America
    • Veit, R. R., Lewis, M. A., 1996. Dispersal, population growth, and the Allee effect: dynamics of the house finch invasion of eastern North America. Am. Nat. 148, 255-274.
    • (1996) Am. Nat. , vol.148 , pp. 255-274
    • Veit, R.R.1    Lewis, M.A.2
  • 52
    • 0348143251 scopus 로고    scopus 로고
    • On spreading speeds and traveling waves for growth and migration in periodic habitat
    • Weinberger, H. F., 2002. On spreading speeds and traveling waves for growth and migration in periodic habitat. J. Math. Biol. 45, 511-548.
    • (2002) J. Math. Biol. , vol.45 , pp. 511-548
    • Weinberger, H.F.1
  • 53
    • 0000384621 scopus 로고
    • Existence and uniqueness of travelling waves in a reaction-diffusion equation with combustion nonlinearity
    • Xin, X., 1991. Existence and uniqueness of travelling waves in a reaction-diffusion equation with combustion nonlinearity. Ind. Univ. Math. J. 40, 995-1008.
    • (1991) Ind. Univ. Math. J. , vol.40 , pp. 995-1008
    • Xin, X.1
  • 54
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • Xin, J., 2000. Front propagation in heterogeneous media. SIAM Rev. 42, 161-230.
    • (2000) SIAM Rev. , vol.42 , pp. 161-230
    • Xin, J.1
  • 55
    • 84893835612 scopus 로고    scopus 로고
    • Sharp asymptotics for KPP pulsating front speed-up and diffusion enhancement by flows
    • (to appear)
    • Zlatos, A., 2010. Sharp asymptotics for KPP pulsating front speed-up and diffusion enhancement by flows. Arch. Rat. Mech. Anal. (to appear).
    • (2010) Arch. Rat. Mech. Anal
    • Zlatos, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.