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Volumn 255, Issue 9, 2008, Pages 2146-2189

Asymptotic spreading in heterogeneous diffusive excitable media

Author keywords

Heterogeneous reaction diffusion equations; Maximum principles; Principal eigenvalues; Propagation and spreading properties

Indexed keywords


EID: 58049150839     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2008.06.030     Document Type: Article
Times cited : (152)

References (31)
  • 1
    • 49349119963 scopus 로고
    • Multidimensional nonlinear diffusions arising in population genetics
    • Aronson D.G., and Weinberger H.F. Multidimensional nonlinear diffusions arising in population genetics. Adv. Math. 30 (1978) 33-76
    • (1978) Adv. Math. , vol.30 , pp. 33-76
    • Aronson, D.G.1    Weinberger, H.F.2
  • 2
    • 58049151473 scopus 로고    scopus 로고
    • M. Bagès, P. Martinez, J.M. Roquejoffre, Dynamique en grand temps pour une classe d'équations de type KPP en milieu périodique, preprint, 2008
    • M. Bagès, P. Martinez, J.M. Roquejoffre, Dynamique en grand temps pour une classe d'équations de type KPP en milieu périodique, preprint, 2008
  • 3
    • 0036298883 scopus 로고    scopus 로고
    • Front propagation in periodic excitable media
    • Berestycki H., and Hamel F. Front propagation in periodic excitable media. Comm. Pure Appl. Math. 55 (2002) 949-1032
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 949-1032
    • Berestycki, H.1    Hamel, F.2
  • 4
    • 53549127849 scopus 로고    scopus 로고
    • Generalized travelling waves for reaction-diffusion equations
    • Perspectives in Nonlinear Partial Differential Equations. In Honor of H. Brezis, Amer. Math. Soc.
    • Berestycki H., and Hamel F. Generalized travelling waves for reaction-diffusion equations. Perspectives in Nonlinear Partial Differential Equations. In Honor of H. Brezis. Contemp. Math. vol. 446 (2007), Amer. Math. Soc. 101-123
    • (2007) Contemp. Math. , vol.446 , pp. 101-123
    • Berestycki, H.1    Hamel, F.2
  • 5
    • 58049174423 scopus 로고    scopus 로고
    • H. Berestycki, F. Hamel, On a general definition of transition waves and their properties, preprint, 2007
    • H. Berestycki, F. Hamel, On a general definition of transition waves and their properties, preprint, 2007
  • 7
    • 41049104617 scopus 로고    scopus 로고
    • Reaction-diffusion equations for population dynamics with forced speed, I: The case of the whole space
    • Berestycki H., and Rossi L. Reaction-diffusion equations for population dynamics with forced speed, I: The case of the whole space. Discrete Contin. Dyn. Syst. 21 (2008) 41-67
    • (2008) Discrete Contin. Dyn. Syst. , vol.21 , pp. 41-67
    • Berestycki, H.1    Rossi, L.2
  • 8
    • 58049159636 scopus 로고    scopus 로고
    • H. Berestycki, L. Rossi, Reaction-diffusion equations for population dynamics with forced speed, II: Cylindrical type domains, preprint, 2008
    • H. Berestycki, L. Rossi, Reaction-diffusion equations for population dynamics with forced speed, II: Cylindrical type domains, preprint, 2008
  • 9
    • 4043174348 scopus 로고    scopus 로고
    • Propagation speed for reaction-diffusion equations in general domains
    • Berestycki H., Hamel F., and Nadirashvili N. Propagation speed for reaction-diffusion equations in general domains. C. R. Acad. Sci. Paris Ser. I 339 (2004) 163-168
    • (2004) C. R. Acad. Sci. Paris Ser. I , vol.339 , pp. 163-168
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 10
    • 16644384785 scopus 로고    scopus 로고
    • The speed of propagation for KPP type problems. I: Periodic framework
    • Berestycki H., Hamel F., and Nadirashvili N. The speed of propagation for KPP type problems. I: Periodic framework. J. Eur. Math. Soc. (JEMS) 7 (2005) 173-213
    • (2005) J. Eur. Math. Soc. (JEMS) , vol.7 , pp. 173-213
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 11
    • 58049149594 scopus 로고    scopus 로고
    • H. Berestycki, F. Hamel, N. Nadirashvili, The speed of propagation for KPP type problems. II: General domains, preprint, 2005
    • H. Berestycki, F. Hamel, N. Nadirashvili, The speed of propagation for KPP type problems. II: General domains, preprint, 2005
  • 12
    • 34247526880 scopus 로고    scopus 로고
    • Liouville-type result for semilinear elliptic equations in unbounded domains
    • Berestycki H., Hamel F., and Rossi L. Liouville-type result for semilinear elliptic equations in unbounded domains. Ann. Mat. Pura Appl. 186 (2007) 469-507
    • (2007) Ann. Mat. Pura Appl. , vol.186 , pp. 469-507
    • Berestycki, H.1    Hamel, F.2    Rossi, L.3
  • 13
    • 84990602584 scopus 로고
    • The principal eigenvalue and maximum principle for second order elliptic operators in general domains
    • Berestycki H., Nirenberg L., and Varadhan S.R.S. The principal eigenvalue and maximum principle for second order elliptic operators in general domains. Comm. Pure Appl. Math. 47 (1994) 47-92
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 14
    • 0000268135 scopus 로고
    • The advance of advantageous genes
    • Fisher R.A. The advance of advantageous genes. Ann. Eugenics 7 (1937) 335-369
    • (1937) Ann. Eugenics , vol.7 , pp. 335-369
    • Fisher, R.A.1
  • 15
    • 4043166736 scopus 로고
    • On wave front propagation in periodic media
    • Stochastic Analysis and Applications. Pinsky M. (Ed)
    • Freidlin M. On wave front propagation in periodic media. In: Pinsky M. (Ed). Stochastic Analysis and Applications. Adv. Probab. Related Topics vol. 7 (1984) 147-166
    • (1984) Adv. Probab. Related Topics , vol.7 , pp. 147-166
    • Freidlin, M.1
  • 16
    • 0008835676 scopus 로고
    • On the propagation of concentration waves in periodic and random media
    • Freidlin M., and Gartner J. On the propagation of concentration waves in periodic and random media. Soviet Math. Dokl. 20 (1979) 1282-1286
    • (1979) Soviet Math. Dokl. , vol.20 , pp. 1282-1286
    • Freidlin, M.1    Gartner, J.2
  • 18
    • 58049170251 scopus 로고    scopus 로고
    • A.N. Kolmogorov, I.G. Petrovsky, N.S. Piskunov, Etude de l équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, in: Bulletin Université d'Etat à Moscou, Bjul. Moskowskogo Gos. Univ., 1937, pp. 1-26
    • A.N. Kolmogorov, I.G. Petrovsky, N.S. Piskunov, Etude de l équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, in: Bulletin Université d'Etat à Moscou, Bjul. Moskowskogo Gos. Univ., 1937, pp. 1-26
  • 19
    • 0039256896 scopus 로고
    • A parabolic equation of the KPP type in higher dimensions
    • Mallordy J.-F., and Roquejoffre J.-M. A parabolic equation of the KPP type in higher dimensions. SIAM J. Math. Anal. 26 1 (1995) 1-20
    • (1995) SIAM J. Math. Anal. , vol.26 , Issue.1 , pp. 1-20
    • Mallordy, J.-F.1    Roquejoffre, J.-M.2
  • 20
    • 58049137779 scopus 로고    scopus 로고
    • H. Matano, Traveling waves in spatially inhomogeneous diffusive media, personal communications
    • H. Matano, Traveling waves in spatially inhomogeneous diffusive media, personal communications
  • 21
    • 58049151787 scopus 로고    scopus 로고
    • A. Mellet, J.-M. Roquejoffre, Construction dondes généralisées pour le modele 1d scalaire à température d'ignition, preprint, 2007
    • A. Mellet, J.-M. Roquejoffre, Construction dondes généralisées pour le modele 1d scalaire à température d'ignition, preprint, 2007
  • 22
    • 58049161360 scopus 로고    scopus 로고
    • G. Nadin, Existence and uniqueness of the solution of a space-time periodic reaction-diffusion equation, preprint, 2007
    • G. Nadin, Existence and uniqueness of the solution of a space-time periodic reaction-diffusion equation, preprint, 2007
  • 23
    • 58049143356 scopus 로고    scopus 로고
    • G. Nadin, The principal eigenvalue of a space-time periodic parabolic operator, Ann. Mat. Pura Appl. (2008), in press
    • G. Nadin, The principal eigenvalue of a space-time periodic parabolic operator, Ann. Mat. Pura Appl. (2008), in press
  • 24
    • 58049159339 scopus 로고    scopus 로고
    • J. Nolen, L. Ryzhik, Traveling waves in a one-dimensional random medium, preprint, 2007
    • J. Nolen, L. Ryzhik, Traveling waves in a one-dimensional random medium, preprint, 2007
  • 25
    • 33845913264 scopus 로고    scopus 로고
    • Variational principle of KPP front speeds in temporally random shear flows with applications
    • Nolen J., and Xin J. Variational principle of KPP front speeds in temporally random shear flows with applications. Comm. Math. Phys. 269 (2007) 459-532
    • (2007) Comm. Math. Phys. , vol.269 , pp. 459-532
    • Nolen, J.1    Xin, J.2
  • 26
    • 58049188100 scopus 로고    scopus 로고
    • J. Nolen, J. Xin, Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows, Ann. Inst. H. Poincaré (2008), in press
    • J. Nolen, J. Xin, Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows, Ann. Inst. H. Poincaré (2008), in press
  • 27
    • 58049168242 scopus 로고    scopus 로고
    • J. Nolen, J. Xin, KPP fronts in 1D random drift, Discrete Contin. Dyn. Syst. Ser. B (2008), in press
    • J. Nolen, J. Xin, KPP fronts in 1D random drift, Discrete Contin. Dyn. Syst. Ser. B (2008), in press
  • 28
    • 33845907733 scopus 로고    scopus 로고
    • Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds
    • Nolen J., Rudd M., and Xin J. Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds. J. Dynam. Partial Differential Equations 2 1 (2005) 1-24
    • (2005) J. Dynam. Partial Differential Equations , vol.2 , Issue.1 , pp. 1-24
    • Nolen, J.1    Rudd, M.2    Xin, J.3
  • 29
    • 58049178288 scopus 로고    scopus 로고
    • Traveling waves in time dependent bistable media
    • Shen W. Traveling waves in time dependent bistable media. Differential Integral Equations 19 3 (2006) 241-278
    • (2006) Differential Integral Equations , vol.19 , Issue.3 , pp. 241-278
    • Shen, W.1
  • 30
    • 0000027176 scopus 로고
    • The behaviour of solutions of some non-linear diffusion equations for large time
    • Uchiyama K. The behaviour of solutions of some non-linear diffusion equations for large time. J. Math. Kyoto Univ. 18 3 (1978) 453-508
    • (1978) J. Math. Kyoto Univ. , vol.18 , Issue.3 , pp. 453-508
    • Uchiyama, K.1
  • 31
    • 0348143251 scopus 로고    scopus 로고
    • On spreading speed and travelling waves for growth and migration models in a periodic habitat
    • Weinberger H. On spreading speed and travelling waves for growth and migration models in a periodic habitat. J. Math. Biol. 45 (2002) 511-548
    • (2002) J. Math. Biol. , vol.45 , pp. 511-548
    • Weinberger, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.