메뉴 건너뛰기




Volumn 42, Issue 1, 2010, Pages 377-405

Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary

Author keywords

Diffusive logistic equation; Free boundary; Invasive population; Spreading vanishing dichotomy

Indexed keywords

CONSTANT SPEED; ELLIPTIC PROBLEM; FREE BOUNDARY; INVASIVE POPULATION; INVASIVE SPECIES; LOGISTIC EQUATIONS; LOGISTIC MODELS; ORIGINAL MODEL; POSITIVE EQUILIBRIUM; SPACE DIMENSIONS; SPREADING SPEED; SPREADING-VANISHING DICHOTOMY;

EID: 77955814290     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/090771089     Document Type: Article
Times cited : (477)

References (31)
  • 2
    • 49349119963 scopus 로고
    • Multidimensional nonlinear diffusions arising in population genetics
    • D. G. ARONSON AND H. F. WEINBERGER, Multidimensional nonlinear diffusions arising in population genetics, Adv. in Math., 30 (1978), pp. 33-76.
    • (1978) Adv. in Math. , vol.30 , pp. 33-76
    • Aronson, D.G.1    Weinberger, H.F.2
  • 3
    • 16644384785 scopus 로고    scopus 로고
    • The speed of propagation for KPP type problems. I. Periodic framework
    • H. BERESTYCKI, F. HAMEL, AND N. NADIRASHVILI, The speed of propagation for KPP type problems. I. Periodic framework, J. Eur. Math. Soc., 7 (2005), pp. 173-213.
    • (2005) J. Eur. Math. Soc. , vol.7 , pp. 173-213
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 4
    • 16644386250 scopus 로고    scopus 로고
    • Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating travelling fronts
    • H. BERESTYCKI, F. HAMEL, AND L. ROQUES, Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating travelling fronts, J. Math. Pures Appl. (9), 84 (2005), pp. 1101-1146.
    • (2005) J. Math. Pures Appl. (9) , vol.84 , pp. 1101-1146
    • Berestycki, H.1    Hamel, F.2    Roques, L.3
  • 5
    • 33947704957 scopus 로고    scopus 로고
    • A geometric approach to free boundary problems
    • American Mathematical Society, Providence, RI
    • L. CAFFARELLI AND S. SALSA, A Geometric Approach to Free Boundary Problems, Grad. Stud. Math. 68, American Mathematical Society, Providence, RI, 2005.
    • (2005) Grad. Stud. Math. , vol.68
    • Caffarelli, L.1    Salsa, S.2
  • 7
    • 0034353709 scopus 로고    scopus 로고
    • A free boundary problem arising in a model of wound healing
    • X. F. CHEN AND A. FRIEDMAN, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), pp. 778-800.
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 778-800
    • Chen, X.F.1    Friedman, A.2
  • 9
    • 0000130586 scopus 로고    scopus 로고
    • N by a squeezing method involving boundary blow-up solutions
    • N by a squeezing method involving boundary blow-up solutions, J. London Math. Soc. (2), 64 (2001), pp. 107-124.
    • (2001) J. London Math. Soc. (2) , vol.64 , pp. 107-124
    • Du, Y.1    Ma, L.2
  • 10
    • 68449103386 scopus 로고    scopus 로고
    • Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem
    • 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), pp. 337-344.
    • (2001) Interfaces Free Bound. , vol.3 , pp. 337-344
    • Fila, M.1    Souplet, P.2
  • 11
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • R. A. FISHER, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), pp. 335-369.
    • (1937) Ann. Eugenics , vol.7 , pp. 335-369
    • Fisher, R.A.1
  • 12
    • 33646853533 scopus 로고    scopus 로고
    • Decay of global solutions, stability and blow-up for a reaction-diffusion problem with free boundary
    • H. GHIDOUCHE, P. SOUPLET, AND D. TARZIA, Decay of global solutions, stability and blow-up for a reaction-diffusion problem with free boundary, Proc. Amer. Math. Soc., 129 (2001), pp. 781-792.
    • (2001) Proc. Amer. Math. Soc. , vol.129 , pp. 781-792
    • Ghidouche, H.1    Souplet, P.2    Tarzia, D.3
  • 14
    • 0037408887 scopus 로고    scopus 로고
    • Vanishing latent heat limit in a Stefan-like problem arising in biology
    • 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), pp. 261-285.
    • (2003) Nonlinear Anal. Real World Appl. , vol.4 , pp. 261-285
    • Hilhorst, D.1    Mimura, M.2    Schätzle, R.3
  • 15
    • 0002722044 scopus 로고
    • Ètude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique
    • A. N. KOLMOGOROV, I. G. PETROVSKY, AND N. S. PISKUNOV, Ètude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bull. Univ. Moscou Sér. Internat., Al (1937), pp. 1-26;
    • (1937) Bull. Univ. Moscou Sér. Internat. , vol.AL , pp. 1-26
    • Kolmogorov, A.N.1    Petrovsky, I.G.2    Piskunov, N.S.3
  • 16
    • 77955787144 scopus 로고
    • English transi
    • P. Peleé (ed.), Academic Press
    • English transi, in Dynamics of Curved Fronts, P. Peleé (ed.), Academic Press, 1988, pp. 105-130.
    • (1988) Dynamics of Curved Fronts , pp. 105-130
  • 18
    • 33751552431 scopus 로고    scopus 로고
    • Asymptotic speeds of spread and traveling waves for monotone semiflows with applications
    • X. LIANG AND X.-Q. ZHAO, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), pp. 1-40.
    • (2007) Comm. Pure Appl. Math. , vol.60 , pp. 1-40
    • Liang, X.1    Zhao, X.-Q.2
  • 19
    • 34547492347 scopus 로고    scopus 로고
    • A free boundary problem for a predator-prey model
    • Z. G. LIN, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), pp. 1883-1892.
    • (2007) Nonlinearity , vol.20 , pp. 1883-1892
    • Lin, Z.G.1
  • 23
    • 84972554209 scopus 로고
    • Stability analysis for free boundary problems in ecology
    • M. MIMURA, Y. YAMADA, AND S. YOTSUTANI, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), pp. 477-498.
    • (1986) Hiroshima Math. J. , vol.16 , pp. 477-498
    • Mimura, M.1    Yamada, Y.2    Yotsutani, S.3
  • 24
    • 84972551309 scopus 로고
    • Free boundary problems for some reactiondiffusion equations
    • M. MIMURA, Y. YAMADA, AND S. YOTSUTANI, Free boundary problems for some reactiondiffusion equations, Hiroshima Math. J., 17 (1987), pp. 241-280.
    • (1987) Hiroshima Math. J. , vol.17 , pp. 241-280
    • Mimura, M.1    Yamada, Y.2    Yotsutani, S.3
  • 25
    • 38249025162 scopus 로고
    • Asymptotic behavior of the solutions of the dead-core problem
    • R. RICCI AND D. A. TARZIA, Asymptotic behavior of the solutions of the dead-core problem, Nonlinear Anal., 13 (1989), pp. 405-411.
    • (1989) Nonlinear Anal. , vol.13 , pp. 405-411
    • Ricci, R.1    Tarzia, D.A.2
  • 28
    • 0009636209 scopus 로고
    • Random dispersal in theoretical populations
    • J. G. SKELLAM, Random dispersal in theoretical populations, Biometrika, 38 (1951), pp. 196-218.
    • (1951) Biometrika , vol.38 , pp. 196-218
    • Skellam, J.G.1
  • 29
    • 0348143251 scopus 로고    scopus 로고
    • On spreading speeds and traveling waves for growth and migration models in a periodic habitat
    • H. F. WEINBERGER, On spreading speeds and traveling waves for growth and migration models in a periodic habitat, J. Math. Biol., 45 (2002), pp. 511-548.
    • (2002) J. Math. Biol. , vol.45 , pp. 511-548
    • Weinberger, H.F.1
  • 30
    • 34547299910 scopus 로고    scopus 로고
    • Anomalous spreading speeds of cooperative recursion systems
    • H. F. WEINBERGER, M. A. LEWIS, AND B. LI, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), pp. 207-222.
    • (2007) J. Math. Biol. , vol.55 , pp. 207-222
    • Weinberger, H.F.1    Lewis, M.A.2    Li, B.3
  • 31
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • J. X. XIN, Front propagation in heterogeneous media, SIAM Rev., 42 (2000), pp. 161-230.
    • (2000) SIAM Rev. , vol.42 , pp. 161-230
    • Xin, J.X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.