Transition fronts for periodic bistable reaction-diffusion equations View Full Text


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Article Info

DATE

2015-11

AUTHORS

Weiwei Ding, François Hamel, Xiao-Qiang Zhao

ABSTRACT

This paper is concerned with the existence and qualitative properties of transition fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. The notion of transition fronts connecting two stable steady states generalizes the standard notion of pulsating fronts. In this paper, we prove that the time-global solutions in the class of transition fronts share some common features. In particular, we establish a uniform estimate for the mean speed of transition fronts, independently of the spatial scale. Under the a priori existence of a pulsating front with nonzero speed or under a more general condition guaranteeing the existence of such a pulsating front, we show that transition fronts are reduced to pulsating fronts, and thus are unique up to shift in time. On the other hand, when the spatial period is large, we also obtain the existence of a new type of transition fronts which are not pulsating fronts. This example, which is the first one in periodic media, shows that even in periodic media, the notion of generalized transition fronts is needed to describe the set of solutions connecting two stable steady states. More... »

PAGES

2517-2551

References to SciGraph publications

  • 1993-12. Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media in JOURNAL OF STATISTICAL PHYSICS
  • 2010-07. Spreading Speeds in Slowly Oscillating Environments in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2001-04. Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1999-01. The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 1991-10. Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 2002-12. On spreading speeds and traveling waves for growth and migration models in a periodic habitat in JOURNAL OF MATHEMATICAL BIOLOGY
  • 1997-07. Traveling Waves in a Convolution Model for Phase Transitions in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1977-12. The approach of solutions of nonlinear diffusion equations to travelling front solutions in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2004-10. Traveling Waves in Diffusive Random Media in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 2013-05. Generalized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2016-06. Front blocking and propagation in cylinders with varying cross section in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2006-10. Entire Solutions with Merging Fronts to Reaction–Diffusion Equations in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 1981. Geometric Theory of Semilinear Parabolic Equations in NONE
  • 2003. Dynamical Systems in Population Biology in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00526-015-0874-6

    DOI

    http://dx.doi.org/10.1007/s00526-015-0874-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046954845


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