메뉴 건너뛰기




Volumn 98, Issue 4, 2012, Pages 428-449

Inside dynamics of pulled and pushed fronts

Author keywords

Pulled fronts; Pushed fronts; Reaction diffusion; Spatial dynamics; Spreading speeds; Traveling fronts

Indexed keywords


EID: 84866150681     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2012.02.005     Document Type: Article
Times cited : (64)

References (39)
  • 1
    • 0002488752 scopus 로고
    • Nonlinear diffusion in population genetics, combustion and nerve propagation
    • Springer, New York, Partial Differential Equations and Related Topics
    • Aronson H.G., Weinberger D.G. Nonlinear diffusion in population genetics, combustion and nerve propagation. Lecture Notes in Math. 1975, vol. 446:5-49. Springer, New York.
    • (1975) Lecture Notes in Math. , vol.446 , pp. 5-49
    • Aronson, H.G.1    Weinberger, D.G.2
  • 2
    • 49349119963 scopus 로고
    • Multidimensional non-linear diffusion arising in population genetics
    • Aronson H.G., Weinberger D.G. Multidimensional non-linear diffusion arising in population genetics. Adv. Math. 1978, 30:33-76.
    • (1978) Adv. Math. , vol.30 , pp. 33-76
    • Aronson, H.G.1    Weinberger, D.G.2
  • 3
    • 84857457388 scopus 로고    scopus 로고
    • Generalized transition waves and their properties
    • Berestycki H., Hamel F. Generalized transition waves and their properties. Commun. Pure Appl. Math. 2012, 65:592-648.
    • (2012) Commun. Pure Appl. Math. , vol.65 , pp. 592-648
    • Berestycki, H.1    Hamel, F.2
  • 4
    • 0002195388 scopus 로고
    • Quelques aspects mathématiques de la propagation des flammes prémélangées
    • Pitman Longman, Harbow, UK, H. Brezis, J.-L. Lions (Eds.) Nonlinear Partial Differential Equations and their Applications
    • Berestycki H., Larrouturou B. Quelques aspects mathématiques de la propagation des flammes prémélangées. Collège de France Seminar 1990, vol. 10:65-129. Pitman Longman, Harbow, UK. H. Brezis, J.-L. Lions (Eds.).
    • (1990) Collège de France Seminar , vol.10 , pp. 65-129
    • Berestycki, H.1    Larrouturou, B.2
  • 5
    • 0000469757 scopus 로고
    • Traveling wave solutions to combustion models and their singular limits
    • Berestycki H., Nicolaenko B., Scheurer B. Traveling wave solutions to combustion models and their singular limits. SIAM J. Math. Anal. 1985, 16:1207-1242.
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 1207-1242
    • Berestycki, H.1    Nicolaenko, B.2    Scheurer, B.3
  • 6
    • 41049104617 scopus 로고    scopus 로고
    • Reaction-diffusion equations for population dynamics with forced speed, I. The case of the whole space
    • Berestycki H., Rossi L. Reaction-diffusion equations for population dynamics with forced speed, I. The case of the whole space. Discrete Contin. Dyn. Syst. 2008, 21:41-67.
    • (2008) Discrete Contin. Dyn. Syst. , vol.21 , pp. 41-67
    • Berestycki, H.1    Rossi, L.2
  • 7
    • 0001778255 scopus 로고
    • The development of traveling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form of traveling waves
    • Billingham J., Needham D.J. The development of traveling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form of traveling waves. Philos. Trans. R. Soc. A 1991, 334:1-24.
    • (1991) Philos. Trans. R. Soc. A , vol.334 , pp. 1-24
    • Billingham, J.1    Needham, D.J.2
  • 8
    • 0003175686 scopus 로고
    • Convergence of Solutions of the Kolmogorov Equation to Travelling Waves
    • Bramson M. Convergence of Solutions of the Kolmogorov Equation to Travelling Waves. Mem. Amer. Math. Soc. 1983.
    • (1983) Mem. Amer. Math. Soc.
    • Bramson, M.1
  • 11
    • 34249762638 scopus 로고
    • The nonlinear stability of front solutions for parabolic differential equations
    • Eckmann J.P., Wayne C.E. The nonlinear stability of front solutions for parabolic differential equations. Comm. Math. Phys. 1994, 161:323-334.
    • (1994) Comm. Math. Phys. , vol.161 , pp. 323-334
    • Eckmann, J.P.1    Wayne, C.E.2
  • 12
    • 0003521963 scopus 로고
    • Mathematical Aspects of Reacting and Diffusing Systems
    • Springer-Verlag
    • Fife P.C. Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomath. 1979, vol. 28. Springer-Verlag.
    • (1979) Lecture Notes in Biomath. , vol.28
    • Fife, P.C.1
  • 13
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to traveling front solutions
    • Fife P.C., McLeod J. The approach of solutions of nonlinear diffusion equations to traveling front solutions. Arch. Ration. Mech. Anal. 1977, 65:335-361.
    • (1977) Arch. Ration. Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.2
  • 14
    • 85082787372 scopus 로고    scopus 로고
    • Ondes progressives dans les sytèmes de reaction-diffusion
    • Cours École d'Été de l'Institut Fourier
    • T. Gallay, Ondes progressives dans les sytèmes de reaction-diffusion, Cours École d'Été de l'Institut Fourier, 2005.
    • (2005)
    • Gallay, T.1
  • 16
    • 0016743943 scopus 로고
    • Travelling fronts in nonlinear diffusion equations
    • Hadeler K., Rothe F. Travelling fronts in nonlinear diffusion equations. J. Math. Biol. 1975, 2:251-263.
    • (1975) J. Math. Biol. , vol.2 , pp. 251-263
    • Hadeler, K.1    Rothe, F.2
  • 17
  • 18
    • 73949088975 scopus 로고    scopus 로고
    • Life at the front of an expanding population
    • Hallatschek O., Nelson D.R. Life at the front of an expanding population. Evolution 2009, 64:193-206.
    • (2009) Evolution , vol.64 , pp. 193-206
    • Hallatschek, O.1    Nelson, D.R.2
  • 19
    • 0040453760 scopus 로고    scopus 로고
    • Reaction-diffusion problems in cylinders with no invariance by translation. Part I: Small perturbations
    • Hamel F. Reaction-diffusion problems in cylinders with no invariance by translation. Part I: Small perturbations. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1997, 14:457-498.
    • (1997) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.14 , pp. 457-498
    • Hamel, F.1
  • 20
    • 0039835893 scopus 로고    scopus 로고
    • Reaction-diffusion problems in cylinders with no invariance by translation. Part II: Monotone perturbations
    • Hamel F. Reaction-diffusion problems in cylinders with no invariance by translation. Part II: Monotone perturbations. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1997, 14:555-596.
    • (1997) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.14 , pp. 555-596
    • Hamel, F.1
  • 21
    • 0003460899 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin
    • Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. 1981, Springer, Berlin.
    • (1981) Lecture Notes in Math.
    • Henry, D.1
  • 22
    • 0002847337 scopus 로고
    • Certain problems of burning-theory equations
    • Kanel' J.I. Certain problems of burning-theory equations. Sov. Math., Dokl. 1961, 2:48-51.
    • (1961) Sov. Math., Dokl. , vol.2 , pp. 48-51
    • Kanel', J.I.1
  • 23
    • 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 N.S., Petrovsky N., Piskunov I.G. Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bull. Univ. État Moscou, Sér. Internat. A 1937, 1:1-26.
    • (1937) Bull. Univ. État Moscou, Sér. Internat. A , vol.1 , pp. 1-26
    • Kolmogorov, N.S.1    Petrovsky, N.2    Piskunov, I.G.3
  • 24
    • 0010697043 scopus 로고
    • On the nonlinear diffusion equation of Kolmogorov, Petrovsky and Piscounov
    • Lau K.S. On the nonlinear diffusion equation of Kolmogorov, Petrovsky and Piscounov. J. Differential Equations 1985, 59:44-70.
    • (1985) J. Differential Equations , vol.59 , pp. 44-70
    • Lau, K.S.1
  • 25
    • 0027524391 scopus 로고
    • Allee dynamics and the spread of invading organisms
    • Lewis M.A., Kareiva P. Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 1993, 43:141-158.
    • (1993) Theor. Popul. Biol. , vol.43 , pp. 141-158
    • Lewis, M.A.1    Kareiva, P.2
  • 26
    • 2442629430 scopus 로고    scopus 로고
    • Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium
    • Lucia M., Muratov C.B., Novaga M. Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium. Comm. Pure Appl. Math. 2004, 57:616-636.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 616-636
    • Lucia, M.1    Muratov, C.B.2    Novaga, M.3
  • 27
    • 65349123850 scopus 로고    scopus 로고
    • Front propagation in infinite cylinders. I. A variational approach
    • Muratov C.B., Novaga M. Front propagation in infinite cylinders. I. A variational approach. Commun. Math. Sci. 2008, 6:799-826.
    • (2008) Commun. Math. Sci. , vol.6 , pp. 799-826
    • Muratov, C.B.1    Novaga, M.2
  • 28
    • 0003475470 scopus 로고    scopus 로고
    • Mathematical Biology
    • Springer-Verlag, New York
    • Murray J.D. Mathematical Biology. Interdiscip. Appl. Math. 2002, vol. 17. Springer-Verlag, New York. third edition.
    • (2002) Interdiscip. Appl. Math. , vol.17
    • Murray, J.D.1
  • 30
    • 33646181600 scopus 로고    scopus 로고
    • Study of the premixed flame model with heat losses the existence of two solutions
    • Roques L. Study of the premixed flame model with heat losses the existence of two solutions. European J. Appl. Math. 2005, 16:741-765.
    • (2005) European J. Appl. Math. , vol.16 , pp. 741-765
    • Roques, L.1
  • 31
    • 0000846626 scopus 로고
    • Convergence to pushed fronts
    • Rothe F. Convergence to pushed fronts. Rocky Mountain J. Math. 1981, 11:617-634.
    • (1981) Rocky Mountain J. Math. , vol.11 , pp. 617-634
    • Rothe, F.1
  • 32
    • 0000814275 scopus 로고
    • On the stability of waves of nonlinear parabolic systems
    • Sattinger D.H. On the stability of waves of nonlinear parabolic systems. Adv. Math. 1976, 22:312-355.
    • (1976) Adv. Math. , vol.22 , pp. 312-355
    • Sattinger, D.H.1
  • 33
    • 0039685238 scopus 로고
    • Weighted norms for the stability of traveling waves
    • Sattinger D.H. Weighted norms for the stability of traveling waves. J. Differential Equations 1977, 25:130-144.
    • (1977) J. Differential Equations , vol.25 , pp. 130-144
    • Sattinger, D.H.1
  • 35
    • 0017172820 scopus 로고
    • On two types of moving front in quasilinear diffusion
    • Stokes A.N. On two types of moving front in quasilinear diffusion. Math. Biosci. 1976, 31:307-315.
    • (1976) Math. Biosci. , vol.31 , pp. 307-315
    • Stokes, A.N.1
  • 36
    • 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. 1978, 18:453-508.
    • (1978) J. Math. Kyoto Univ. , vol.18 , pp. 453-508
    • Uchiyama, K.1
  • 37
    • 0142119503 scopus 로고    scopus 로고
    • Front propagation into unstable states
    • van Saarloos W. Front propagation into unstable states. Phys. Rep. 2003, 386:29-222.
    • (2003) Phys. Rep. , vol.386 , pp. 29-222
    • van Saarloos, W.1
  • 39
    • 3142757050 scopus 로고    scopus 로고
    • Enhanced (hydrodynamic) transport induced by population growth in reaction-diffusion systems with application to population genetics
    • Vlad M.O., Cavalli-Sforza L.L., Ross J. Enhanced (hydrodynamic) transport induced by population growth in reaction-diffusion systems with application to population genetics. Proc. Natl. Acad. Sci. 2004, 101:10249-10253.
    • (2004) Proc. Natl. Acad. Sci. , vol.101 , pp. 10249-10253
    • Vlad, M.O.1    Cavalli-Sforza, L.L.2    Ross, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.