Affiliation:
1. School of Applied Mathematics Shanxi University of Finance and Economics Taiyuan China
2. School of Mathematical Sciences Shanxi University Taiyuan China
3. School of Science Beijing University of Chemical Technology Beijing China
Abstract
This paper is concerned with the nonlinear stability of forced traveling waves for a Lotka–Volterra cooperative model under climate change. Firstly, by applying the
‐weighted energy estimate method, the comparison principle, and the squeezing technique, we investigate that all forced traveling waves with the speed
are exponentially stable in the form of
for some
. Secondly, in order to improve the former results, we take another weight function and construct the related different weighted Sobolev space. Instead of the
‐weighted energy estimate, we first establish a
‐weighted energy estimate in the weighted Sobolev space. Then, by using this crucial
‐estimate, we further obtain the desired
‐energy estimate. Finally, we obtain that all forced traveling waves with the speed
are exponentially stable in the form of
for some
, where
.
Funder
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics
Cited by
3 articles.
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