Stability of traveling fronts in a population model with nonlocal delay and advection

Li Liu; Yun-Rui Yang; Shou-Peng Zhang

doi:10.26637/mjm304/008

Abstract

In this paper, we are concerned with the stability of traveling fronts in a population model with nonlocal delay and advection under the large initial perturbation (i.e. the initial perturbation around the traveling wave decays exponentially as $x \rightarrow-\infty$, but it can be arbitrarily large in other locations). The globally exponential stability of traveling fronts is established by the weighted-energy method combining with comparison principle, including even the slower waves whose wave speed are close to the critical speed.

Keywords:

Traveling fronts, stability, weighted-energy method

Mathematics Subject Classification:

34G20

Authors Imprint References Funding Related Articles Downloads

Li Liu chool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu-730070, P.R. China.
Yun-Rui Yang School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu-730070, P.R. China.
Shou-Peng Zhang School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu-730070, P.R. China.

Pages: 498-510
Date Published: 01-10-2015
Vol. 3 No. 04 (2015): Malaya Journal of Matematik (MJM)

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Supported by the NSF of China (11301241), Science and Technology Plan Foundation of Gansu Province of China (145RJYA250), Institutions of higher learning scientific research project of Gansu Province of China (2013A-044).