Generalized fronts for one-dimensional reaction-diffusion equations

Discrete and Continuous Dynamical Systems

Volumn 26, Issue 1, 2010, Pages 303-312

  Mellet, Antoine ^a   Roquejoffre, Jean Michel ^b   Latp, Yannick Sire ^c,d  

^a UNIVERSITY OF MARYLAND   (United States)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^c AIX MARSEILLE UNIVERSITY   (France)

^d Laboratoire Poncelet   (Russian Federation)

Author keywords

Fronts propagation; Heterogeneous media; Reaction diffusion equations

Indexed keywords

EID: 76849093212     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2010.26.303     Document Type: Article

References (10)

1. H. Berestycki and F. Hamel, Front propagation in periodic excitable media, Comm. Pure Appl. Math., 55 (2002), 949-1032.
2. H. Berestycki and F. Hamel, Generalized travelling waves for reaction-diffusion equations, in "Perspectives in Nonlinear Partial Differential Equations," 101-123. Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007.
3. H. Berestycki, B. Larrouturou and P.-L. Lions, Multi-dimensional travelling-wave solutions of a flame propagation model, Arch. Rat. Mech. Anal, 111 (1990), 33-49.
4. H. Berestycki, B. Nicolaenko and B. Scheurer, Traveling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal., 16 (1985), 1207-1242.
5. H. Berestycki and L. Nirenberg, Travelling fronts in cylinders, Ann. Inst. H. Poincaré Anal. Non Linéaire, 5 (1992), 497-572.
6. J. Nolen and L. Ryzhik, Traveling waves in a one-dimensional heterogeneous medium, Annales de l'institut Henri Poincare - Analyse Non Lineaire, 26 no.3 (2009), 1021-1047.
7. A. Mellet, J. Nolen, J.-M. Roquejoffre and L. Ryzhik, Stability of generalized transition fronts, Comm. in P.D.E., 34 ( 2009), 521-552.
8. W. Shen, Traveling waves in diffusive random media, J. Dynam. Differential Equations, 16 (2004), 1011-1060.
9. J. X. Xin, Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rational Mech. Anal., 121 (1992), 205-233.
10. J. X. Xin, Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media, J. Statist. Phys., 73 (1993), 893-926.