메뉴 건너뛰기




Volumn 184, Issue 2, 2011, Pages 405-453

Effect of noise on front propagation in reaction-diffusion equations of KPP type

Author keywords

Random traveling fronts; Reaction diffusion equation; Stochastic partial differential equations; White noise

Indexed keywords


EID: 79955048916     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-010-0292-5     Document Type: Article
Times cited : (102)

References (35)
  • 6
    • 84980189802 scopus 로고
    • Maximal displacement of branching Brownian motion
    • Bramson, M.: Maximal displacement of branching Brownian motion. Commun. Pure Appl. Math. 31(5), 531-581 (1978).
    • (1978) Commun. Pure Appl. Math. , vol.31 , Issue.5 , pp. 531-581
    • Bramson, M.1
  • 7
    • 0003175686 scopus 로고
    • Convergence of solutions of the Kolmogorov equation to travelling waves
    • 285iv+190
    • Bramson, M.: Convergence of solutions of the Kolmogorov equation to travelling waves. Mem. Am. Math. Soc. 44, 285 (1983). iv+190.
    • (1983) Mem. Am. Math. Soc. , vol.44
    • Bramson, M.1
  • 8
    • 0000532118 scopus 로고
    • A simple proof of the stability criterion of Gray and Griffeath
    • Bramson, M., Durrett, R.: A simple proof of the stability criterion of Gray and Griffeath. Probab. Theory Relat. Fields 80(2), 293-298 (1988).
    • (1988) Probab. Theory Relat. Fields , vol.80 , Issue.2 , pp. 293-298
    • Bramson, M.1    Durrett, R.2
  • 9
    • 0001425072 scopus 로고    scopus 로고
    • Shift in the velocity of a front due to a cutoff
    • Brunet, E., Derrida, B.: Shift in the velocity of a front due to a cutoff. Phys. Rev. E (3), Part A 56(3), 2597-2604 (1997).
    • (1997) Phys. Rev. E (3), Part A , vol.56 , Issue.3 , pp. 2597-2604
    • Brunet, E.1    Derrida, B.2
  • 10
    • 0035532616 scopus 로고    scopus 로고
    • Effect of microscopic noise on front propagation
    • Brunet, E., Derrida, B.: Effect of microscopic noise on front propagation. J. Stat. Phys. 103(1-2), 269-282 (2001).
    • (2001) J. Stat. Phys. , vol.103 , Issue.1-2 , pp. 269-282
    • Brunet, E.1    Derrida, B.2
  • 11
    • 33744469315 scopus 로고    scopus 로고
    • A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
    • Brunet, E., Derrida, B., Mueller, A. H., Munier, S.: A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts. Phys. Rev. E 73, 056126 (2006).
    • (2006) Phys. Rev. E , vol.73 , pp. 056126
    • Brunet, E.1    Derrida, B.2    Mueller, A.H.3    Munier, S.4
  • 12
    • 26044474668 scopus 로고    scopus 로고
    • On travelling waves for the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov equation
    • Conlon, J., Doering, C.: On travelling waves for the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov equation. J. Stat. Phys. 120(3-4), 421-477 (2005).
    • (2005) J. Stat. Phys. , vol.120 , Issue.3-4 , pp. 421-477
    • Conlon, J.1    Doering, C.2
  • 13
    • 33947384615 scopus 로고    scopus 로고
    • The critical wave speed for the Fisher-Kolmogorov-Petrowskii-Piscounov equation with cut-off
    • Dumortier, F., Popovic, N., Kaper, T.: The critical wave speed for the Fisher-Kolmogorov-Petrowskii-Piscounov equation with cut-off. Nonlinearity 20(4), 855-877 (2007).
    • (2007) Nonlinearity , vol.20 , Issue.4 , pp. 855-877
    • Dumortier, F.1    Popovic, N.2    Kaper, T.3
  • 14
    • 0000808186 scopus 로고
    • Oriented percolation in two dimensions
    • Durrett, R.: Oriented percolation in two dimensions. Ann. Probab. 12, 999-1040 (1984).
    • (1984) Ann. Probab. , vol.12 , pp. 999-1040
    • Durrett, R.1
  • 15
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • Fisher, R. A.: The wave of advance of advantageous genes. Ann. Eugen. 7, 355-369 (1937).
    • (1937) Ann. Eugen. , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 16
    • 0011522309 scopus 로고
    • Edge fluctuations for the one-dimensional supercritical contact process
    • Galves, A., Presutti, E.: Edge fluctuations for the one-dimensional supercritical contact process. Ann. Probab. 15(3), 1131-1145 (1987).
    • (1987) Ann. Probab. , vol.15 , Issue.3 , pp. 1131-1145
    • Galves, A.1    Presutti, E.2
  • 18
    • 4944240975 scopus 로고    scopus 로고
    • On stationary distributions for the KPP equation with branching noise
    • Horridge, P., Tribe, R.: On stationary distributions for the KPP equation with branching noise. Ann. Inst. H. Poincar Probab. Stat. 40(6), 759-770 (2004).
    • (2004) Ann. Inst. H. Poincar Probab. Stat. , vol.40 , Issue.6 , pp. 759-770
    • Horridge, P.1    Tribe, R.2
  • 19
    • 0002722044 scopus 로고
    • Étude de l'Equation de la diffusion avec croissance de la quantité de mati'ere et son application 'a un probl'eme biologique
    • Kolmogorov, A., Petrovsky, I., Piskunov, N.: Étude de l'Equation de la diffusion avec croissance de la quantité de mati'ere et son application 'a un probl'eme biologique. Mosc. Univ., Bull. Math. 1, 1-25 (1937).
    • (1937) Mosc. Univ., Bull. Math. , vol.1 , pp. 1-25
    • Kolmogorov, A.1    Petrovsky, I.2    Piskunov, N.3
  • 20
    • 0001371280 scopus 로고    scopus 로고
    • Front propagation:precursors, cutoffs and structural stability
    • Kessler, Z., Ner, D. A., Sander, L. M.: Front propagation: precursors, cutoffs and structural stability. Phys. Rev. E 58, 107-114 (1998).
    • (1998) Phys. Rev. E , vol.58 , pp. 107-114
    • Kessler, Z.1    Ner, D.A.2    Sander, L.M.3
  • 22
    • 84980187449 scopus 로고
    • Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov
    • McKean, H. P.: Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Commun. Pure Appl. Math. 28(3), 323-331 (1975).
    • (1975) Commun. Pure Appl. Math. , vol.28 , Issue.3 , pp. 323-331
    • McKean, H.P.1
  • 23
    • 84980134415 scopus 로고
    • A Correction to: "Application of Brownian motion to the equation of Kolmogorov-Petrovski-Piskunov [sic]"
    • McKean, H. P.: A Correction to: "Application of Brownian motion to the equation of Kolmogorov-Petrovski-Piskunov [sic]". Commun. Pure Appl. Math. 29(5), 553-554 (1976).
    • (1976) Commun. Pure Appl. Math. , vol.29 , Issue.5 , pp. 553-554
    • McKean, H.P.1
  • 24
    • 79954997302 scopus 로고    scopus 로고
    • Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case
    • Mytnik, L., Perkins, E.: Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case. To appear in Probab. Theory Relat. Fields.
    • To appear in Probab. Theory Relat. Fields
    • Mytnik, L.1    Perkins, E.2
  • 25
    • 33845485683 scopus 로고    scopus 로고
    • On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
    • Mytnik, L., Perkins, E., Sturm, A.: On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients. Ann. Probab. 34, 1910-1959 (2006).
    • (2006) Ann. Probab. , vol.34 , pp. 1910-1959
    • Mytnik, L.1    Perkins, E.2    Sturm, A.3
  • 26
    • 0001419936 scopus 로고
    • The compact support property for solutions to the heat equation with noise
    • Mueller, C., Perkins, E.: The compact support property for solutions to the heat equation with noise. Probab. Theory Relat. Fields 93(3), 325-358 (1992).
    • (1992) Probab. Theory Relat. Fields , vol.93 , Issue.3 , pp. 325-358
    • Mueller, C.1    Perkins, E.2
  • 27
    • 0038101626 scopus 로고
    • Random traveling waves for the KPP equation with noise
    • Mueller, C., Sowers, R.: Random traveling waves for the KPP equation with noise. J. Funct. Anal. 128, 439-498 (1995).
    • (1995) J. Funct. Anal. , vol.128 , pp. 439-498
    • Mueller, C.1    Sowers, R.2
  • 28
    • 21844524825 scopus 로고
    • Stochastic p.d.e.'s arising from the long range contact and long range voter processes
    • Mueller, C., Tribe, R.: Stochastic p. d. e.'s arising from the long range contact and long range voter processes. Probab. Theory Relat. Fields 102(4), 519-546 (1995).
    • (1995) Probab. Theory Relat. Fields , vol.102 , Issue.4 , pp. 519-546
    • Mueller, C.1    Tribe, R.2
  • 31
    • 0037659276 scopus 로고
    • Stochastic partial differential equations, a review
    • Pardoux, E.: Stochastic partial differential equations, a review. Bull. Sci. Math. 117(1), 29-47 (1993).
    • (1993) Bull. Sci. Math. , vol.117 , Issue.1 , pp. 29-47
    • Pardoux, E.1
  • 32
    • 0001215656 scopus 로고    scopus 로고
    • Interfacial velocity corrections due to multiplicative noise
    • Pechenik, L., Levine, H.: Interfacial velocity corrections due to multiplicative noise. Phys. Rev. E 59, 3893-3900 (1999).
    • (1999) Phys. Rev. E , vol.59 , pp. 3893-3900
    • Pechenik, L.1    Levine, H.2
  • 33
    • 0002128531 scopus 로고
    • Stepping stone models in population genetics and population dynamics
    • S. Albeverio (Ed.), Dordrecht: Reidel
    • Shiga, T.: Stepping stone models in population genetics and population dynamics. In: Albeverio, S., et al. (eds.) Stochastic Processes in Physics and Engineering, pp. 345-355. Reidel, Dordrecht (1988).
    • (1988) Stochastic Processes in Physics and Engineering , pp. 345-355
    • Shiga, T.1
  • 34
    • 0142119503 scopus 로고    scopus 로고
    • Front propagation into unstable states
    • van Saarloos, W.: Front propagation into unstable states. Phys. Rep. 386, 29-222 (2003).
    • (2003) Phys. Rep. , vol.386 , pp. 29-222
    • van Saarloos, W.1
  • 35
    • 0000659593 scopus 로고
    • An introduction to stochastic partial differential equations
    • Lecture Notes in Mathematics, P. L. Hennequin (Ed.), Berlin: Springer
    • Walsh, J. B.: An introduction to stochastic partial differential equations. In: Hennequin, P. L. (ed.) École d'été de probabilités de Saint-Flour, XIV-1984. Lecture Notes in Mathematics, vol. 1180, pp. 265-439. Springer, Berlin (1986).
    • (1986) École D'été De probabilités De Saint-Flour, XIV-1984 , vol.1180 , pp. 265-439
    • Walsh, J.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.