메뉴 건너뛰기




Volumn 89, Issue 4, 2008, Pages 355-399

Qualitative properties of monostable pulsating fronts: exponential decay and monotonicity

Author keywords

Asymptotic behavior; Fronts; Qualitative properties; Semilinear parabolic equations

Indexed keywords


EID: 41149173181     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2007.12.005     Document Type: Article
Times cited : (133)

References (53)
  • 1
    • 41149145517 scopus 로고    scopus 로고
    • M. Bages, Dynamique non triviale en temps pour une équation de type KPP en milieu périodique, PhD thesis, 2007
    • M. Bages, Dynamique non triviale en temps pour une équation de type KPP en milieu périodique, PhD thesis, 2007
  • 2
    • 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
  • 3
    • 41149143006 scopus 로고    scopus 로고
    • H. Berestycki, F. Hamel, Reaction-Diffusion Equations and Propagation Phenomena, Applied Mathematical Sciences, Springer-Verlag, 2008, in press
    • H. Berestycki, F. Hamel, Reaction-Diffusion Equations and Propagation Phenomena, Applied Mathematical Sciences, Springer-Verlag, 2008, in press
  • 4
    • 11944266033 scopus 로고    scopus 로고
    • The principal eigenvalue of elliptic operators with large drift and applications to nonlinear propagation phenomena
    • Berestycki H., Hamel F., and Nadirashvili N. The principal eigenvalue of elliptic operators with large drift and applications to nonlinear propagation phenomena. Comm. Math. Phys. 253 (2005) 451-480
    • (2005) Comm. Math. Phys. , vol.253 , pp. 451-480
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 5
    • 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. 7 (2005) 173-213
    • (2005) J. Eur. Math. Soc. , vol.7 , pp. 173-213
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 6
    • 22244440170 scopus 로고    scopus 로고
    • Analysis of the periodically fragmented environment model. I. Species persistence
    • Berestycki H., Hamel F., and Roques L. Analysis of the periodically fragmented environment model. I. Species persistence. J. Math. Biol. 51 (2005) 75-113
    • (2005) J. Math. Biol. , vol.51 , pp. 75-113
    • Berestycki, H.1    Hamel, F.2    Roques, L.3
  • 7
    • 16644386250 scopus 로고    scopus 로고
    • Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating traveling fronts
    • Berestycki H., Hamel F., and Roques L. Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating traveling fronts. J. Math. Pures Appl. 84 (2005) 1101-1146
    • (2005) J. Math. Pures Appl. , vol.84 , pp. 1101-1146
    • Berestycki, H.1    Hamel, F.2    Roques, L.3
  • 8
    • 0002626724 scopus 로고
    • Multidimensional traveling-wave solutions of a flame propagation model
    • Berestycki H., Larrouturou B., and Lions P.-L. Multidimensional traveling-wave solutions of a flame propagation model. Arch. Ration. Mech. Anal. 111 (1990) 33-49
    • (1990) Arch. Ration. Mech. Anal. , vol.111 , pp. 33-49
    • Berestycki, H.1    Larrouturou, B.2    Lions, P.-L.3
  • 9
    • 13844311748 scopus 로고
    • On the method of moving planes and the sliding method
    • Berestycki H., and Nirenberg L. On the method of moving planes and the sliding method. Bol. Soc. Bras. Mat. 22 (1991) 1-37
    • (1991) Bol. Soc. Bras. Mat. , vol.22 , pp. 1-37
    • Berestycki, H.1    Nirenberg, L.2
  • 11
    • 2442636449 scopus 로고    scopus 로고
    • Singular limit and homogenization for flame propagation in periodic excitable media
    • Caffarelli L.A., Lee K.-A., and Mellet A. Singular limit and homogenization for flame propagation in periodic excitable media. Arch. Ration. Mech. Anal. 172 (2004) 153-190
    • (2004) Arch. Ration. Mech. Anal. , vol.172 , pp. 153-190
    • Caffarelli, L.A.1    Lee, K.-A.2    Mellet, A.3
  • 12
    • 33644999049 scopus 로고    scopus 로고
    • Homogenization and flame propagation in periodic excitable media: the asymptotic speed of propagation
    • Caffarelli L.A., Lee K.-A., and Mellet A. Homogenization and flame propagation in periodic excitable media: the asymptotic speed of propagation. Comm. Pure Appl. Math. 59 (2006) 501-525
    • (2006) Comm. Pure Appl. Math. , vol.59 , pp. 501-525
    • Caffarelli, L.A.1    Lee, K.-A.2    Mellet, A.3
  • 13
    • 0031352502 scopus 로고    scopus 로고
    • Homogenization of periodic structures via Bloch decomposition
    • Conca C., and Vanninathan M. Homogenization of periodic structures via Bloch decomposition. SIAM J. Appl. Math. 57 (1997) 1639-1659
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1639-1659
    • Conca, C.1    Vanninathan, M.2
  • 14
    • 41149086566 scopus 로고    scopus 로고
    • M. El Smaily, Pulsating traveling fronts: Asymptotics and homogenization regimes, preprint
    • M. El Smaily, Pulsating traveling fronts: Asymptotics and homogenization regimes, preprint
  • 15
    • 41149156275 scopus 로고    scopus 로고
    • M. El Smaily, F. Hamel, L. Roques, Homogenization and influence of fragmentation in a biological invasion model, preprint
    • M. El Smaily, F. Hamel, L. Roques, Homogenization and influence of fragmentation in a biological invasion model, preprint
  • 16
    • 0003299218 scopus 로고
    • Mathematical Aspects of Reacting and Diffusing Systems
    • Springer-Verlag
    • Fife P.C. Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomathematics vol. 28 (1979), Springer-Verlag
    • (1979) Lecture Notes in Biomathematics , vol.28
    • Fife, P.C.1
  • 17
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to traveling front solutions
    • Fife P.C., and McLeod J.B. The approach of solutions of nonlinear diffusion equations to traveling front solutions. Arch. Ration. Mech. Anal. 65 (1977) 335-361
    • (1977) Arch. Ration. Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 18
    • 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
  • 19
    • 41149108933 scopus 로고    scopus 로고
    • G. Fréjacques, Travelling waves in infinite cylinders with time-periodic coefficients, PhD thesis, 2005
    • G. Fréjacques, Travelling waves in infinite cylinders with time-periodic coefficients, PhD thesis, 2005
  • 20
    • 0039140304 scopus 로고
    • Harnack inequalities for solutions of general second order parabolic equations and estimates of their Hölder constants
    • 23-43
    • Gruber M. Harnack inequalities for solutions of general second order parabolic equations and estimates of their Hölder constants. Math. Z. 185 (1984) pp 23-43
    • (1984) Math. Z. , vol.185
    • Gruber, M.1
  • 21
    • 33744731512 scopus 로고    scopus 로고
    • Front propagation for discrete periodic monostable equations
    • Guo J.-S., and Hamel F. Front propagation for discrete periodic monostable equations. Math. Ann. 335 (2006) 489-525
    • (2006) Math. Ann. , vol.335 , pp. 489-525
    • Guo, J.-S.1    Hamel, F.2
  • 22
    • 41149115964 scopus 로고    scopus 로고
    • F. Hamel, L. Roques, Uniqueness and stability properties of monostable pulsating fronts, preprint
    • F. Hamel, L. Roques, Uniqueness and stability properties of monostable pulsating fronts, preprint
  • 23
    • 41149117015 scopus 로고    scopus 로고
    • S. Heinze, Homogenization of flame fronts, preprint IWR, Heidelberg, 1993
    • S. Heinze, Homogenization of flame fronts, preprint IWR, Heidelberg, 1993
  • 24
    • 23044530485 scopus 로고    scopus 로고
    • Wave solution for reaction-diffusion systems in perforated domains
    • Heinze S. Wave solution for reaction-diffusion systems in perforated domains. Z. Anal. Anwendungen 20 (2001) 661-670
    • (2001) Z. Anal. Anwendungen , vol.20 , pp. 661-670
    • Heinze, S.1
  • 25
    • 41149106229 scopus 로고    scopus 로고
    • S. Heinze, Large convection limits for KPP fronts, preprint
    • S. Heinze, Large convection limits for KPP fronts, preprint
  • 26
    • 0141970998 scopus 로고
    • Existence of traveling waves for reaction-diffusion equations of Fisher type in periodic media
    • World Scientific
    • Hudson W., and Zinner B. Existence of traveling waves for reaction-diffusion equations of Fisher type in periodic media. Boundary Problems for Functional Differential Equations (1995), World Scientific 187-199
    • (1995) Boundary Problems for Functional Differential Equations , pp. 187-199
    • Hudson, W.1    Zinner, B.2
  • 29
    • 0041132744 scopus 로고
    • An estimate for the probability of a diffusion process hitting a set of positive measure
    • Krylov N.V., and Safonov M.V. An estimate for the probability of a diffusion process hitting a set of positive measure. Dokl. Akad. Nauka SSSR 245 (1979) 18-20
    • (1979) Dokl. Akad. Nauka SSSR , vol.245 , pp. 18-20
    • Krylov, N.V.1    Safonov, M.V.2
  • 31
    • 84954678370 scopus 로고    scopus 로고
    • Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, II
    • Levermore C.D., and Xin J.X. Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, II. Comm. Partial Differential Equations 17 (1999) 1901-1924
    • (1999) Comm. Partial Differential Equations , vol.17 , pp. 1901-1924
    • Levermore, C.D.1    Xin, J.X.2
  • 32
    • 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 (1995) 1-20
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 1-20
    • Mallordy, J.-F.1    Roquejoffre, J.-M.2
  • 33
    • 41149144019 scopus 로고    scopus 로고
    • H. Matano, Traveling waves in spatially inhomogeneous diffusive media-The nonperiodic case, preprint
    • H. Matano, Traveling waves in spatially inhomogeneous diffusive media-The nonperiodic case, preprint
  • 35
    • 41149143488 scopus 로고    scopus 로고
    • G. Nadin, Travelling fronts in space-time periodic media, preprint
    • G. Nadin, Travelling fronts in space-time periodic media, preprint
  • 36
    • 41149140737 scopus 로고    scopus 로고
    • K.-I. Nakamura, Effective speed of traveling wavefronts in periodic inhomogeneous media, in: Proc. Workshop Nonlinear Partial Differential Equations and Related Topics, Joint Research Center for Science and Technology of Ryukoku University, 1999, pp. 53-60
    • K.-I. Nakamura, Effective speed of traveling wavefronts in periodic inhomogeneous media, in: Proc. Workshop Nonlinear Partial Differential Equations and Related Topics, Joint Research Center for Science and Technology of Ryukoku University, 1999, pp. 53-60
  • 37
    • 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. Dyn. Part. Diff. Eq. 2 (2005) 1-24
    • (2005) Dyn. Part. Diff. Eq. , vol.2 , pp. 1-24
    • Nolen, J.1    Rudd, M.2    Xin, J.3
  • 38
    • 21244461106 scopus 로고    scopus 로고
    • Reaction-diffusion front speeds in spatially-temporally periodic shear flows
    • Nolen J., and Xin J. Reaction-diffusion front speeds in spatially-temporally periodic shear flows. SIAM Multi. Model. Simul. 1 (2003) 554-570
    • (2003) SIAM Multi. Model. Simul. , vol.1 , pp. 554-570
    • Nolen, J.1    Xin, J.2
  • 39
    • 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., and Xin J. Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle. Disc. Cont. Dyn. Syst. 13 (2005) 1217-1234
    • (2005) Disc. Cont. Dyn. Syst. , vol.13 , pp. 1217-1234
    • Nolen, J.1    Xin, J.2
  • 40
    • 33847266469 scopus 로고    scopus 로고
    • Boundary layers and KPP fronts in a cellular flow
    • Novikov A., and Ryzhik L. Boundary layers and KPP fronts in a cellular flow. Arch. Ration. Mech. Anal. 184 (2007) 23-48
    • (2007) Arch. Ration. Mech. Anal. , vol.184 , pp. 23-48
    • Novikov, A.1    Ryzhik, L.2
  • 41
    • 0040970045 scopus 로고
    • Second order elliptic operators with periodic coefficients: criticality theory, perturbations, and positive harmonic functions
    • Pinsky R. Second order elliptic operators with periodic coefficients: criticality theory, perturbations, and positive harmonic functions. J. Funct. Anal. 129 (1995) 80-107
    • (1995) J. Funct. Anal. , vol.129 , pp. 80-107
    • Pinsky, R.1
  • 42
    • 0000728498 scopus 로고    scopus 로고
    • Eventual monotonicity and convergence to traveling fronts for the solutions of parabolic equations in cylinders
    • Roquejoffre J.-M. Eventual monotonicity and convergence to traveling fronts for the solutions of parabolic equations in cylinders. Ann. Inst. H. Poincaré, Anal. Non Lin. 14 (1997) 499-552
    • (1997) Ann. Inst. H. Poincaré, Anal. Non Lin. , vol.14 , pp. 499-552
    • Roquejoffre, J.-M.1
  • 43
    • 35348956875 scopus 로고    scopus 로고
    • KPP pulsating front speed-up by flows
    • Ryzhik L., and Zlatos A. KPP pulsating front speed-up by flows. Commun. Math. Sci. 5 (2007) 575-593
    • (2007) Commun. Math. Sci. , vol.5 , pp. 575-593
    • Ryzhik, L.1    Zlatos, A.2
  • 47
    • 0348143251 scopus 로고    scopus 로고
    • On spreading speeds and traveling waves for growth and migration in periodic habitat
    • Weinberger H.F. On spreading speeds and traveling waves for growth and migration in periodic habitat. J. Math. Biol. 45 (2002) 511-548
    • (2002) J. Math. Biol. , vol.45 , pp. 511-548
    • Weinberger, H.F.1
  • 49
    • 0000384621 scopus 로고
    • Existence and uniqueness of traveling waves in a reaction-diffusion equation with combustion nonlinearity
    • Xin X. Existence and uniqueness of traveling waves in a reaction-diffusion equation with combustion nonlinearity. Idiana Univ. Math. J. 40 (1991) 985-1008
    • (1991) Idiana Univ. Math. J. , vol.40 , pp. 985-1008
    • Xin, X.1
  • 50
    • 0002125162 scopus 로고
    • Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity
    • Xin X. Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity. J. Dyn. Diff. Eq. 3 (1991) 541-573
    • (1991) J. Dyn. Diff. Eq. , vol.3 , pp. 541-573
    • Xin, X.1
  • 51
    • 21144464889 scopus 로고
    • Existence of planar flame fronts in convective-diffusive periodic media
    • Xin X. Existence of planar flame fronts in convective-diffusive periodic media. Arch. Ration. Mech. Anal. 121 (1992) 205-233
    • (1992) Arch. Ration. Mech. Anal. , vol.121 , pp. 205-233
    • Xin, X.1
  • 52
    • 0034206088 scopus 로고    scopus 로고
    • Analysis and modeling of front propagation in heterogeneous media
    • Xin J.X. Analysis and modeling of front propagation in heterogeneous media. SIAM Review 42 (2000) 161-230
    • (2000) SIAM Review , vol.42 , pp. 161-230
    • Xin, J.X.1
  • 53
    • 41149122486 scopus 로고    scopus 로고
    • A. Zlatos, Sharp asymptotics for KPP pulsating front speed-up and diffusion enhancement by flows, preprint
    • A. Zlatos, Sharp asymptotics for KPP pulsating front speed-up and diffusion enhancement by flows, preprint


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.