메뉴 건너뛰기




Volumn 19, Issue 3, 2012, Pages 73-101

Traveling wave solutions of spatially periodic nonlocal monostable equations

Author keywords

Monostable equation; Nonlocal dispersal; Principal eigenfunction; Principal eigenvalue; Random dispersal; Spreading speed; Traveling wave solution

Indexed keywords


EID: 84863968232     PISSN: 1074133X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (63)

References (37)
  • 1
    • 34147185183 scopus 로고    scopus 로고
    • Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal
    • P. Bates and G. Zhao, Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl. 332(2007), 428-440.
    • (2007) J. Math. Anal. Appl. , vol.332 , pp. 428-440
    • Bates, P.1    Zhao, G.2
  • 2
    • 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), 172-213.
    • (2005) J. Eur. Math. Soc. , vol.7 , pp. 172-213
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 3
    • 77749289459 scopus 로고    scopus 로고
    • The speed of propagation for KPP type problems, II - General domains
    • H. Berestycki, F. Hamel, and N. Nadirashvili, The speed of propagation for KPP type problems, II - General domains, J. Amer. Math. Soc. 23(1) (2010), 1-34
    • (2010) J. Amer. Math. Soc. , vol.23 , Issue.1 , pp. 1-34
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 4
    • 22244440170 scopus 로고    scopus 로고
    • Analysis of the periodically fragmented environment model: I - Species persistence
    • DOI 10.1007/s00285-004-0313-3
    • H. Berestycki, F. Hamel, and L. Roques, Analysis of periodically fragmented environment model: I-Species persistence, J. Math. Biol. 51(2005), 75-113. (Pubitemid 40991322)
    • (2005) Journal of Mathematical Biology , vol.51 , Issue.1 , pp. 75-113
    • Berestycki, H.1    Hamel, F.2    Roques, L.3
  • 5
    • 16644386250 scopus 로고    scopus 로고
    • Analysis of the periodically fragmented environment model: II - Biological invasions and pulsating travelling fronts
    • DOI 10.1016/j.matpur.2004.10.006, PII S0021782404001345
    • H. Berestycki, F. Hamel, and L. Roques, Analysis of periodically fragmented environment model: II - Biological invasions and pulsating traveling fronts, J. Math. Pures Appl. 84(2005), 1101-1146. (Pubitemid 41051951)
    • (2005) Journal des Mathematiques Pures et Appliquees , vol.84 , Issue.8 , pp. 1101-1146
    • Berestycki, H.1    Hamel, F.2    Roques, L.3
  • 6
  • 7
    • 0037144960 scopus 로고    scopus 로고
    • Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations
    • X. Chen and J.-S. Guo, Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations, J. Diff. Eq. 184(2) (2002), 549-569.
    • (2002) J. Diff. Eq. , vol.184 , Issue.2 , pp. 549-569
    • Chen, X.1    Guo, J.-S.2
  • 8
    • 34548337269 scopus 로고    scopus 로고
    • On uniqueness and monotonicity of solutions of non-local reaction diffusion equation
    • J. Coville, On uniqueness and monotonicity of solutions of non-local reaction diffusion equation, Ann. Mat. Pura Appl. 185(3) (2006), 461-485
    • (2006) Ann. Mat. Pura Appl. , vol.185 , Issue.3 , pp. 461-485
    • Coville, J.1
  • 9
    • 77956344620 scopus 로고    scopus 로고
    • On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators
    • J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators, J. Differential Equations 249(2010), 2921-2953.
    • (2010) J. Differential Equations , vol.249 , pp. 2921-2953
    • Coville, J.1
  • 11
    • 52649153528 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity
    • J. Coville, J. Dávila, and S. Martínez, Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity, SIAM J. Math. Anal. 39(2008), 1693-1709.
    • (2008) SIAM J. Math. Anal. , vol.39 , pp. 1693-1709
    • Coville, J.1    Dávila, J.2    Martínez, S.3
  • 12
    • 43049112828 scopus 로고    scopus 로고
    • Nonlocal anisotropic dispersal with monostable nonlinearity
    • J. Coville, J. Dávila, and S. Martínez, Nonlocal anisotropic dispersal with monostable nonlinearity, J. Differential Equations 244(2008), 3080-3118.
    • (2008) J. Differential Equations , vol.244 , pp. 3080-3118
    • Coville, J.1    Dávila, J.2    Martínez, S.3
  • 13
    • 12444337556 scopus 로고    scopus 로고
    • Propagation speed of travelling fronts in non local reaction-diffusion equations
    • DOI 10.1016/j.na.2003.10.030, PII S0362546X0400241X
    • J. Coville and L. Dupaigne, Propagation speed of travelling fronts in non local reactiondiffusion equations, Nonlinear Analysis 60(2005), 797-819. (Pubitemid 40142396)
    • (2005) Nonlinear Analysis, Theory, Methods and Applications , vol.60 , Issue.5 , pp. 797-819
    • Coville, J.1    Dupaigne, L.2
  • 15
    • 34249873628 scopus 로고    scopus 로고
    • An integrodifferential analog of semilinear parabolic PDEs, Partial differential equations and applications
    • Dekker, New York
    • P. C. Fife, An integrodifferential analog of semilinear parabolic PDEs, Partial differential equations and applications, Lecture Notes in Pure and Appl. Math., 177, pp. 137-145, Dekker, New York, 1996.
    • (1996) Lecture Notes in Pure and Appl. Math. , vol.177 , pp. 137-145
    • Fife, P.C.1
  • 16
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • R. Fisher, The wave of advance of advantageous genes, Ann. of Eugenics 7(1937), 335-369.
    • (1937) Ann. of Eugenics , vol.7 , pp. 335-369
    • Fisher, R.1
  • 17
    • 0008835676 scopus 로고
    • On the propagation of concentration waves in periodic and ramdom media
    • M. Freidlin and J. Gärtner, On the propagation of concentration waves in periodic and ramdom media, Soviet Math. Dokl. 20(1979), 1282-1286.
    • (1979) Soviet Math. Dokl. , vol.20 , pp. 1282-1286
    • Freidlin, M.1    Gärtner, J.2
  • 18
    • 55249116542 scopus 로고    scopus 로고
    • On the principal eigenvalue of some nonlocal diffusion problems
    • J. García-Melán and J. D. Rossi, On the principal eigenvalue of some nonlocal diffusion problems, J. Differential Equations 246(2009), 21-38.
    • (2009) J. Differential Equations , vol.246 , pp. 21-38
    • García-Melán, J.1    Rossi, J.D.2
  • 19
    • 63449133914 scopus 로고    scopus 로고
    • Uniqueness and stability of traveling waves for periodic monostable lattice dynamical system
    • J.-S. Guo and C.-C. Wu, Uniqueness and stability of traveling waves for periodic monostable lattice dynamical system, J. Differential Equations 246(2009), 3818-3833.
    • (2009) J. Differential Equations , vol.246 , pp. 3818-3833
    • Guo, J.-S.1    Wu, C.-C.2
  • 20
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer-Verlag, Berlin
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, 1981.
    • (1981) Lecture Notes in Math. , pp. 840
    • Henry, D.1
  • 21
    • 84879751555 scopus 로고    scopus 로고
    • Zhang, Effects of spatial variations and dispersal strategies on principal eigenvalues of dispersal operators and spreading speeds of monostable equations
    • A, to appear
    • G. Hetzer, W. Shen, and A. Zhang, Effects of spatial variations and dispersal strategies on principal eigenvalues of dispersal operators and spreading speeds of monostable equations, Rocky Mountain Journal of Mathematics, to appear.
    • Rocky Mountain Journal of Mathematics
    • Hetzer, G.1    Shen, W.2
  • 22
    • 0141970998 scopus 로고
    • Existence of traveling waves for reaction diffusion equations of Fisher type in periodic media
    • World Sci. Publ., River Edge, NJ
    • W. Hudson and B. Zinner, Existence of traveling waves for reaction diffusion equations of Fisher type in periodic media, Boundary value problems for functional-differential equations, pp. 187-199, World Sci. Publ., River Edge, NJ, 1995.
    • (1995) Boundary Value Problems for Functional-differential Equations , pp. 187-199
    • Hudson, W.1    Zinner, B.2
  • 23
    • 50249123097 scopus 로고    scopus 로고
    • Spectral theory for nonlocal dispersal with periodic or almost-periodic time dependence
    • V. Hutson, W. Shen and G. T. Vickers, Spectral theory for nonlocal dispersal with periodic or almost-periodic time dependence, Rocky Mountain Journal of Mathematics 38(2008), 1147-1175.
    • (2008) Rocky Mountain Journal of Mathematics , vol.38 , pp. 1147-1175
    • Hutson, V.1    Shen, W.2    Vickers, G.T.3
  • 24
    • 0002722044 scopus 로고
    • A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem
    • A. Kolmogorov, I. Petrowsky, and N. Piscunov, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Bjul. Moskovskogo Gos. Univ., 1(1937), 1-26.
    • (1937) Bjul. Moskovskogo Gos. Univ. , vol.1 , pp. 1-26
    • Kolmogorov, A.1    Petrowsky, I.2    Piscunov, N.3
  • 25
    • 76549124055 scopus 로고    scopus 로고
    • Entire solutions in the Fisher-KPP equation with nonlocal dispersal
    • W.-T. Li, Y.-J. Sun, Z.-C. Wang, Entire solutions in the Fisher-KPP equation with nonlocal dispersal, Nonlinear Analysis: Real World Appl., 11(4) (2010), 2302-2313.
    • (2010) Nonlinear Analysis: Real World Appl. , vol.11 , Issue.4 , pp. 2302-2313
    • Li, W.-T.1    Sun, Y.-J.2    Wang, Z.-C.3
  • 26
    • 33751552431 scopus 로고    scopus 로고
    • Asymptotic speeds of spread and traveling waves for monotone semiflows with applications
    • DOI 10.1002/cpa.20154
    • X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math. 60(1) (2007), 1-40. (Pubitemid 44832314)
    • (2007) Communications on Pure and Applied Mathematics , vol.60 , Issue.1 , pp. 1-40
    • Liang, X.1    Zhao, X.-Q.2
  • 27
    • 77953124191 scopus 로고    scopus 로고
    • Spreading speeds and traveling waves for abstract monostable evolution systems
    • X. Liang and X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, Journal of Functional Analysis 259(2010), 857-903.
    • (2010) Journal of Functional Analysis , vol.259 , pp. 857-903
    • Liang, X.1    Zhao, X.-Q.2
  • 29
    • 68849091810 scopus 로고    scopus 로고
    • Traveling fronts in space-time periodic media
    • G. Nadin, Traveling fronts in space-time periodic media, J. Math. Pures Appl. (9) 92(2009), 232-262.
    • (2009) J. Math. Pures Appl. , vol.92 , Issue.9 , pp. 232-262
    • Nadin, G.1
  • 30
    • 33845907733 scopus 로고    scopus 로고
    • Existence of KPP fronts in spatially-temporally periodic adevction and variational principle for propagation speeds
    • J. Nolen, M. Rudd, and J. Xin, Existence of KPP fronts in spatially-temporally periodic adevction and variational principle for propagation speeds, Dynamics of PDE 2(2005), 1-24.
    • (2005) Dynamics of PDE , vol.2 , pp. 1-24
    • Nolen, J.1    Rudd, M.2    Xin, J.3
  • 31
    • 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
    • Recent Development on Differential Equations and Dynamical Systems Part II
    • J. Nolen and J. Xin, Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle, Discrete and Continuous Dynamical Systems 13(2005), 1217-1234. (Pubitemid 41730766)
    • (2005) Discrete and Continuous Dynamical Systems , vol.13 , Issue.5 , pp. 1217-1234
    • Nolen, J.1    Xin, J.2
  • 32
    • 73249127366 scopus 로고    scopus 로고
    • Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay
    • S. Pan, W.-T. Li, and G. Lin, Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay, Nonlinear Analysis: Theory, Methods & Applications 72(2010), 3150-3158.
    • (2010) Nonlinear Analysis: Theory, Methods & Applications , vol.72 , pp. 3150-3158
    • Pan, S.1    Li, W.-T.2    Lin, G.3
  • 34
    • 33846862020 scopus 로고    scopus 로고
    • Spectral theory for general nonautonomous/random dispersal evolution operators
    • W. Shen and G. T. Vickers, Spectral theory for general nonautonomous/random dispersal evolution operators, J. Differential Equations 235(2007), 262-297.
    • (2007) J. Differential Equations , vol.235 , pp. 262-297
    • Shen, W.1    Vickers, G.T.2
  • 35
    • 77952951758 scopus 로고    scopus 로고
    • Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats
    • W. Shen and A. Zhang, Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats, Journal of Differential Equations 249(2010), 747-795.
    • (2010) Journal of Differential Equations , vol.249 , pp. 747-795
    • Shen, W.1    Zhang, A.2
  • 36
    • 84856177831 scopus 로고    scopus 로고
    • Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats
    • W. Shen and A. Zhang, Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats, Proceedings of the American Math. Soc. 140(2012), 1681-1696.
    • (2012) Proceedings of the American Math. Soc. , vol.140 , pp. 1681-1696
    • Shen, W.1    Zhang, A.2
  • 37
    • 0348143251 scopus 로고    scopus 로고
    • On spreading speeds and traveling waves for growth and migration models in a periodic habitat
    • DOI 10.1007/s00285-002-0169-3
    • 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. (Pubitemid 44200145)
    • (2002) Journal of Mathematical Biology , vol.45 , Issue.6 , pp. 511-548
    • Weinberger, H.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.