Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Traveling curved fronts in monotone bistable systems

Pages: 2339 - 2374, Volume 32, Issue 6, June 2012      doi:10.3934/dcds.2012.32.2339

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Zhi-Cheng Wang - School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)

Abstract: This paper is concerned with the existence, uniqueness and stability of traveling curved fronts for reaction-diffusion bistable systems in two-dimensional space. By establishing the comparison theorem and constructing appropriate supersolutions and subsolutions, we prove the existence of traveling curved fronts. Furthermore, we show that the curved front is globally stable. Finally, we apply the results to three important models in biology.

Keywords:  Reaction-diffusion system, traveling curved front, bistable, existence, stability.
Mathematics Subject Classification:  35K57, 35B35, 35B40.

Received: January 2011;      Revised: October 2011;      Available Online: February 2012.