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Volumn 1, Issue 4, 2004, Pages 605-626

PATTERN FORMATION, WAVE PROPAGATION AND STABILITY IN CONSERVATION LAWS WITH SLOW DIFFUSION AND FAST REACTION

Author keywords

asymptotic stability; pattern formation; Reaction diffusion convection equations; transition fronts

Indexed keywords


EID: 40249107710     PISSN: 02198916     EISSN: 17936993     Source Type: Journal    
DOI: 10.1142/S0219891604000275     Document Type: Article
Times cited : (3)

References (24)
  • 1
    • 0018480694 scopus 로고
    • A microscopic theory for anti phase motion and its application to anti phase domain coarsening
    • S. Allen and J. Cahn, A microscopic theory for anti phase motion and its application to anti phase domain coarsening, Acta Metal. 27 (1979) 1084–1095.
    • (1979) Acta Metal , vol.27 , pp. 1084-1095
    • Allen, S.1    Cahn, J.2
  • 2
    • 84942222028 scopus 로고
    • The zero set of a solution of a parabolic equation
    • S. Angenent, The zero set of a solution of a parabolic equation, J. Reine Angew. Math. 390 (1988) 79–86.
    • (1988) J. Reine Angew. Math , vol.390 , pp. 79-86
    • Angenent, S.1
  • 3
    • 84990575560 scopus 로고
    • On the slowness of phase boundary motion in one space dimension
    • L. Bronsard and R. V. Kohn, On the slowness of phase boundary motion in one space dimension, Comm. Pure Appl. Math. 43 (1990) 983–997.
    • (1990) Comm. Pure Appl. Math , vol.43 , pp. 983-997
    • Bronsard, L.1    Kohn, R. V.2
  • 4
    • 0032386084 scopus 로고    scopus 로고
    • A new approach to front propagation problems: theory and applications
    • G. Barles and P. E. Souganidis, A new approach to front propagation problems: theory and applications, Arch. Ration. Mech. Anal. 141 (1998) 237–296.
    • (1998) Arch. Ration. Mech. Anal , vol.141 , pp. 237-296
    • Barles, G.1    Souganidis, P. E.2
  • 5
    • 84990619184 scopus 로고
    • Metastable patterns in solutions of ut = εuxx−f(u)
    • J. Carr and P. L. Pego, Metastable patterns in solutions of ut = εuxx−f(u), Comm. Pure Appl. Math. 42 (1989) 523–576.
    • (1989) Comm. Pure Appl. Math , vol.42 , pp. 523-576
    • Carr, J.1    Pego, P. L.2
  • 6
    • 0001249829 scopus 로고
    • Generation and propagation of interfaces in reaction–diffusion systems
    • X. Chen, Generation and propagation of interfaces in reaction–diffusion systems, J. Differential Equations 96 (1992) 116–142.
    • (1992) J. Differential Equations , vol.96 , pp. 116-142
    • Chen, X.1
  • 7
    • 85189324504 scopus 로고    scopus 로고
    • Front motion in multi-dimensional conservation laws with stiff source terms driven by mean curvature and variation of front thickness
    • to appear in
    • H. T. Fan and S. Jin, Front motion in multi-dimensional conservation laws with stiff source terms driven by mean curvature and variation of front thickness, to appear in Q. Appl. Math.
    • Q. Appl. Math.
    • Fan, H. T.1    Jin, S.2
  • 8
    • 0037457009 scopus 로고    scopus 로고
    • Wave patterns and slow motions in inviscid and viscous hyperbolic equations with stiff reaction terms
    • H. T. Fan, S. Jin and J. Miller, Wave patterns and slow motions in inviscid and viscous hyperbolic equations with stiff reaction terms, J. Differential Equations 89 (2003) 267–291.
    • (2003) J. Differential Equations , vol.89 , pp. 267-291
    • Fan, H. T.1    Jin, S.2    Miller, J.3
  • 9
    • 0034634860 scopus 로고    scopus 로고
    • Zero reaction limit for hyperbolic conservation laws with source terms
    • H. Fan, S. Jin and Z.-H. Teng, Zero reaction limit for hyperbolic conservation laws with source terms, J. Difference Equations 168 (2000) 270–294.
    • (2000) J. Difference Equations , vol.168 , pp. 270-294
    • Fan, H.1    Jin, S.2    Teng, Z.-H.3
  • 10
    • 0002626726 scopus 로고
    • The generation and propagation of internal layers
    • P. C. Fife and L. Hsiao, The generation and propagation of internal layers, Nonlinear Anal. 12 (1988) 19–41.
    • (1988) Nonlinear Anal , vol.12 , pp. 19-41
    • Fife, P. C.1    Hsiao, L.2
  • 11
    • 0000268135 scopus 로고
    • The wave of advance of advantageous
    • R. A. Fisher, The wave of advance of advantageous, Ann. Eugenics 7 (1937) 355–369.
    • (1937) Ann. Eugenics , vol.7 , pp. 355-369
    • Fisher, R. A.1
  • 12
    • 0001863910 scopus 로고
    • Slow motion manifolds, dormant instability, and singular perturbations
    • G. Fusco and J. K. Hale, Slow motion manifolds, dormant instability, and singular perturbations, J. Dynam. Differential Equations 1 (1989) 75–94.
    • (1989) J. Dynam. Differential Equations , vol.1 , pp. 75-94
    • Fusco, G.1    Hale, J. K.2
  • 13
    • 0036230229 scopus 로고    scopus 로고
    • Variational principles for propagation speeds in inhomogeneous media
    • S. Heinze, G. Papanicolaou and A. Stevens, Variational principles for propagation speeds in inhomogeneous media, SIAM J. Appl. Math. 62 (2001) 129–143.
    • (2001) SIAM J. Appl. Math , vol.62 , pp. 129-143
    • Heinze, S.1    Papanicolaou, G.2    Stevens, A.3
  • 14
    • 0012783397 scopus 로고    scopus 로고
    • Viscous profiles for traveling waves of scalar balance laws: the uniformly hyperbolic case
    • J. Hrterich, Viscous profiles for traveling waves of scalar balance laws: the uniformly hyperbolic case, Electron. J. Differential Equations 20 (2000) 22.
    • (2000) Electron. J. Differential Equations , vol.20 , pp. 22
    • Hrterich, J.1
  • 15
    • 0002722044 scopus 로고
    • Etude de l’equation de la diffusion avec croissane de la quantité de matiére et son applilation á un probleme biologique
    • A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Etude de l’equation de la diffusion avec croissane de la quantité de matiére et son applilation á un probleme biologique, Moskow Univ. Math. Bull. 1 (1937) 1–25.
    • (1937) Moskow Univ. Math. Bull , vol.1 , pp. 1-25
    • Kolmogorov, A. N.1    Petrovsky, I. G.2    Piskunov, N. S.3
  • 16
    • 0036572049 scopus 로고    scopus 로고
    • First order singular perturbations of quasilinear nonconvex type
    • C. Mascia, First order singular perturbations of quasilinear nonconvex type, J. Differential Equations 181 (2002) 31–57.
    • (2002) J. Differential Equations , vol.181 , pp. 31-57
    • Mascia, C.1
  • 17
    • 0000657925 scopus 로고
    • Nonincrease of the lap number of a solution for a one-dimensional semi-linear parabolic equations
    • H. Matano, Nonincrease of the lap number of a solution for a one-dimensional semi-linear parabolic equations J. Fac. Sci. Univ. Tokyo. Sect. IA Math. 29(2) (1982) 401–441.
    • (1982) J. Fac. Sci. Univ. Tokyo. Sect. IA Math , vol.29 , Issue.2 , pp. 401-441
    • Matano, H.1
  • 18
    • 84941507534 scopus 로고
    • Gestaltaussagen über Lösungen parabolischer Differentialgleichungen
    • K. Nickel, Gestaltaussagen über Lösungen parabolischer Differentialgleichungen, J. Reine Angew. Math. 211 (1962) 78–94.
    • (1962) J. Reine Angew. Math , vol.211 , pp. 78-94
    • Nickel, K.1
  • 19
    • 44749084234 scopus 로고
    • Fronts moving with curvature dependent speed: Algorithm based on Hamilton–Jacobi equations
    • S. Osher and J. Sethian, Fronts moving with curvature dependent speed: Algorithm based on Hamilton–Jacobi equations, J. Comput. Phys. 79 (1988) 12–49.
    • (1988) J. Comput. Phys , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.2
  • 20
    • 85189300626 scopus 로고    scopus 로고
    • On stability of traveling waves of Burgers–Fisher equation
    • J. Pan and H. L. Liu, On stability of traveling waves of Burgers–Fisher equation, Ann. Differential Equations 14 (1998) 37–47.
    • (1998) Ann. Differential Equations , vol.14 , pp. 37-47
    • Pan, J.1    Liu, H. L.2
  • 21
  • 22
    • 0000814275 scopus 로고
    • On the stability of waves of nonlinear parabolic systems
    • D. H. Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. Math. 22 (1976) 312–355.
    • (1976) Adv. Math , vol.22 , pp. 312-355
    • Sattinger, D. H.1
  • 23
    • 0003913993 scopus 로고
    • Traveling Wave Solutions of Parabolic Systems
    • (AMS, Providence, RI)
    • A. Volpert, V. Volpert and V. Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monographs 140 (AMS, Providence, RI, 1994).
    • (1994) Transl. Math. Monographs , vol.140
    • Volpert, A.1    Volpert, V.2    Volpert, V.3
  • 24
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • J. Xin, Front propagation in heterogeneous media, SIAM Rev. 42 (2000) 161–230.
    • (2000) SIAM Rev , vol.42 , pp. 161-230
    • Xin, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.