Travelingcurved fronts in monotone bistable systems

Zhi-Cheng Wang

doi:10.3934/dcds.2012.32.2339

Article Contents

2012, Volume 32, Issue 6: 2339-2374. Doi: 10.3934/dcds.2012.32.2339

This issue Previous Article Well-posedness and stabilization of an Euler-Bernoulli equation with a localized nonlinear dissipation involving the $p$-Laplacian Next Article

Traveling curved fronts in monotone bistable systems

Zhi-Cheng Wang^1,

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received: December 31, 2010

Revised: September 30, 2011

Published: May 2012

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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.

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Mathematics Subject Classification: 35K57, 35B35, 35B40.

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