Generalized Fronts for One-dimensional Reaction-diffusion Equations

@inproceedings{Mellet2009GeneralizedFF,
  title={Generalized Fronts for One-dimensional Reaction-diffusion Equations},
  author={Antoine Mellet and Jean-Michel Roquejoffre},
  year={2009}
}
For a class of one-dimensional reaction-diffusion equations, we establish the existence of generalized fronts, as recently defined by Berestycki and Hamel. We also prove uniform nondegeneracy estimates, such as a lower bound on the time derivative on some level sets, as well as a lower bound on the spatial derivative. 
Highly Cited
This paper has 26 citations. REVIEW CITATIONS

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
16 Extracted Citations
7 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-7 of 7 references

Front propagation in periodic excitable media

  • H. Berestycki, F. Hamel
  • Comm. Pure Appl. Math., 55
  • 2002
Highly Influential
4 Excerpts

Traveling waves in diffusive random media

  • W. Shen
  • J. Dynam. Differential Equations, 16
  • 2004
1 Excerpt

Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media

  • J. X. Xin
  • J. Statist. Phys. 73
  • 1993
1 Excerpt

Existence of planar flame fronts in convective-diffusive periodic media

  • J. X. Xin
  • Arch. Rational Mech. Anal. 121
  • 1992
1 Excerpt

Multi-dimensional travelling-wave solutions of a flame propagation model

  • H. Berestycki, B. Larrouturou, P.-L. Lions
  • Arch. Rat. Mech. Anal, 111
  • 1990
1 Excerpt

Traveling wave solutions to combustion models and their singular limits

  • H. Berestycki, B. Nicolaenko, B. Scheurer
  • SIAM J. Math. Anal. 16
  • 1985
2 Excerpts

Similar Papers

Loading similar papers…