Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems
نویسندگان
چکیده
We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection–reaction–diffusion systems. Under certain conditions, we prove that there exists a maximal wave speed c∗ such that for each wave speed c ≤ c∗, there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c ≤ c∗ are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves with speed c > c∗. © 2014 Elsevier Inc. All rights reserved. MSC: 35B10; 35B35; 35B40; 35C07; 35K40
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