Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 28, Issue -, Pages 48-71Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2015.09.006
Keywords
Reaction-advection-diffusion equations; Periodic media; Pulsating fronts; Asymptotic behavior; Entire solution
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Funding
- NSF of China [11371179, 11201402]
- NSF of Shandong Province of China [ZR2010AQ006]
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This paper is concerned with the reaction-advection-diffusion equations with bistable nonlinearity in periodic media. Assume that the equation has three equilibria: an unstable equilibrium 61 and two stable equilibria 0 and 1. It is known that there exist different pulsating fronts connecting any two of those three equilibria. In this paper we first study the exponential behavior of the fronts when they approach their stable limiting states. Then, we establish three different types of pulsating entire solutions for the equation. To establish the existence of entire solutions, we consider combinations of any two of those different pulsating fronts and construct appropriate sub- and supersolutions. (C) 2015 Elsevier Ltd. All rights reserved.
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