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Volumn 34, Issue 6, 2009, Pages 521-552

Stability of generalized transition fronts

Author keywords

Generalized fronts; Stability

Indexed keywords


EID: 69049104527     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300902768677     Document Type: Article
Times cited : (46)

References (27)
  • 1
    • 0036298883 scopus 로고    scopus 로고
    • Front propagation in periodic excitable media
    • Berestycki, H., Hamel, F. (2002). Front propagation in periodic excitable media. Comm. Pure Appl. Math. 55:949-1032.
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 949-1032
    • Berestycki, H.1    Hamel, F.2
  • 3
    • 69049110000 scopus 로고    scopus 로고
    • Bistable travelling waves around an obstacle
    • In press
    • Berestycki, H., Hamel, F., Matano, H. (2008). Bistable travelling waves around an obstacle. Comm. Pure Appl. Math. In press.
    • (2008) Comm. Pure Appl. Math.
    • Berestycki, H.1    Hamel, F.2
  • 4
    • 0002043417 scopus 로고
    • Asymptotic behaviour via the Harnack inequality
    • In: Ambrosetti, A., ed, Quaderni Sc. Norm, Pisa
    • Berestycki, H., Nirenberg, L. (1991). Asymptotic behaviour via the Harnack inequality. In: Ambrosetti, A., ed. Nonlinear Analysis, a Tribute in Honour of G. Prodi, Pisa: Quaderni Sc. Norm., pp. 135-144.
    • (1991) Nonlinear Analysis, a Tribute in Honour of G. Prodi , pp. 135-144
    • Berestycki, H.1    Nirenberg, L.2
  • 6
    • 0001203924 scopus 로고    scopus 로고
    • Existence, uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations
    • Chen, X. (1997). Existence, uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations. Adv. Diff. Eq. 2:125-160.
    • (1997) Adv. Diff. Eq. , vol.2 , pp. 125-160
    • Chen, X.1
  • 7
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations by travelling front solutions
    • Fife, P. C., McLeod, J. B. (1977). The approach of solutions of nonlinear diffusion equations by travelling front solutions. Arch. Rat. Mech. Anal. 65:335-361.
    • (1977) Arch. Rat. Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 8
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • Fisher, R. (1937). The wave of advance of advantageous genes. Ann. Eugenics 7:355-369.
    • (1937) Ann. Eugenics , vol.7 , pp. 355-369
    • Fisher, R.1
  • 10
    • 2942625416 scopus 로고    scopus 로고
    • Stability of travelling fronts in a two-dimensional model for conical flames
    • Hamel, F., Monneau, R., Roquejoffre, J.-M. (2004). Stability of travelling fronts in a two-dimensional model for conical flames. Ann. Sci. Ec. Norm. Sup 37:469-506.
    • (2004) Ann. Sci. Ec. Norm. Sup , vol.37 , pp. 469-506
    • Hamel, F.1    Monneau, R.2    Roquejoffre, J.-M.3
  • 11
    • 0011219720 scopus 로고
    • Laminar flame theory and the steady, linear burning of a monopropellant
    • Johnson, W. E., Nachbar, W. (1963). Laminar flame theory and the steady, linear burning of a monopropellant. Arch. Rational Mech. Anal. 12:58-92.
    • (1963) Arch. Rational Mech. Anal. , vol.12 , pp. 58-92
    • Johnson, W.E.1    Nachbar, W.2
  • 12
    • 0000638913 scopus 로고
    • Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory
    • (In Russian)
    • Kanel', J. (1962) Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory. (In Russian). Mat. Sb. (N.S.), 59:101, pp. 245-288.
    • (1962) Mat. Sb. (N.S.) , vol.59-101 , pp. 245-288
    • Kanel', J.1
  • 13
    • 69049091006 scopus 로고
    • Stabilization of solutions of the Cauchy problem for certain linear parabolic equations
    • (In Russian)
    • Kanel', J. (1963). Stabilization of solutions of the Cauchy problem for certain linear parabolic equations. (In Russian). Uspehi Mat. Nauk 18(110):127-134.
    • (1963) Uspehi Mat. Nauk , vol.18 , Issue.110 , pp. 127-134
    • Kanel', J.1
  • 14
    • 0003913874 scopus 로고
    • I. Stabilization of the solutions of the equations of combustion theory with finite initial functions
    • (In Russian)
    • Kanel', J. (1964). I. Stabilization of the solutions of the equations of combustion theory with finite initial functions. (In Russian). Mat. Sb. (N.S.) 65(107):398-413.
    • (1964) Mat. Sb. (N.S.) , vol.65 , Issue.107 , pp. 398-413
    • Kanel', J.1
  • 15
    • 0002722044 scopus 로고
    • E´tude de l'équation de la chaleur avec accroissement matiére et son application á un probléme biologique
    • (See [20] pp. 105-130 for an English translation.)
    • Kolmogorov, A. N., Petrovskii, I. G., Piskunov, N. S. (1937). E´tude de l'équation de la chaleur avec accroissement matiére et son application á un probléme biologique [Study of the heat material equation and its applications to a biology problem]. Bull. Moskov. Gos. Univ. Mat. Mekh. 1:1-25. (See [20] pp. 105-130 for an English translation.)
    • (1937) Bull. Moskov. Gos. Univ. Mat. Mekh. , vol.1 , pp. 1-25
    • Kolmogorov, A.N.1    Petrovskii, I.G.2    Piskunov, N.S.3
  • 16
    • 0034456883 scopus 로고    scopus 로고
    • Wave-block in excitable media due to regions of depressed excitability
    • Lewis, T. J., Keener, J. P. (2000). Wave-block in excitable media due to regions of depressed excitability. SIAM J. Appl. Math. 61:293-316.
    • (2000) SIAM JAppl. Math. , vol.61 , pp. 293-316
    • Lewis, T.J.1    Keener, J.P.2
  • 17
    • 69049088938 scopus 로고    scopus 로고
    • A talk presented at IHP
    • Paris, September
    • Matano, H. (2002). A talk presented at IHP, Paris, September, 2002.
    • (2002)
    • Matano, H.1
  • 19
    • 69049096261 scopus 로고    scopus 로고
    • Traveling waves in a one-dimensional heterogeneous medium
    • Nolen, J., Ryzhik, L. (2008). Traveling waves in a one-dimensional heterogeneous medium. Ann. IHP, Analyse Non Linéaire.
    • (2008) Analyse Non Linéaire
    • Nolen, J.1    Ryzhik, L.2
  • 20
    • 0004243252 scopus 로고
    • P. Pelcé, Ed., Academic Press
    • Dynamics of curved fronts, P. Pelcé, Ed., Academic Press, 1988.
    • (1988) Dynamics of curved fronts
  • 21
    • 34250074344 scopus 로고
    • Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations
    • Polacˇcik, P., Tereščák, I. (1993). Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. J. Dynam. Diff. Eq. 5:279-303.
    • (1993) J. Dynam. Diff. Eq. , vol.5 , pp. 279-303
    • Polac&caron1    cik, P.2    Tereščák, I.3
  • 22
    • 69049120890 scopus 로고
    • Comportement asymptotique des solutions d'une classe d'équations paraboliques semi-linéaires
    • Roquejoffre, J.-M. (1993). Comportement asymptotique des solutions d'une classe d'équations paraboliques semi-linéaires [Asymptotic behavior of the solutions of a class of semilinear parabolic equations]. C.R. Acad. Sci. Paris 316:461-464.
    • (1993) Acad. Sci. Paris , vol.316 , pp. 461-464
    • Roquejoffre, J.-M.1
  • 23
    • 0000728498 scopus 로고    scopus 로고
    • Eventual monotonicity and convergence to travelling waves in a class of seminlinear parabolic equations in cylinders
    • Roquejoffre, J.-M. (1997). Eventual monotonicity and convergence to travelling waves in a class of seminlinear parabolic equations in cylinders. Ann. IHP, Analyse Non Linéaire 14:499-552.
    • (1997) Ann. IHP, Analyse Non Linéaire , vol.14 , pp. 499-552
    • Roquejoffre, J.-M.1
  • 24
    • 0000814275 scopus 로고
    • Stability of waves of nonlinear parabolic equations
    • Sattinger, D. H. (1976). Stability of waves of nonlinear parabolic equations. Adv. Math. 22:312-355.
    • (1976) Adv. Math. , vol.22 , pp. 312-355
    • Sattinger, D.H.1
  • 25
    • 33845908811 scopus 로고    scopus 로고
    • Traveling waves in diffusive random media
    • Shen, W. (2004). Traveling waves in diffusive random media. J. Dynamics Diff. Eqns. 16:1011-1060.
    • (2004) J. Dynamics Diff. Eqns. , vol.16 , pp. 1011-1060
    • Shen, W.1
  • 26
    • 0034206088 scopus 로고    scopus 로고
    • Analysis and modelling of front propagation in heterogeneous media
    • Xin, J. (2000). Analysis and modelling of front propagation in heterogeneous media. SIAM Rev. 42:161-230.
    • (2000) SIAM Rev. , vol.42 , pp. 161-230
    • Xin, J.1
  • 27
    • 69049118312 scopus 로고    scopus 로고
    • Preprint
    • Zlatos, A. (2009). Preprint.
    • (2009)
    • Zlatos, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.