期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 35, 期 5, 页码 1843-1872出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2015.35.1843
关键词
Reaction diffusion equations; travelling waves; forced speed; energy functional; long time behaviour
资金
- European Research Council under the European Union's Seventh Framework Program (FP)/ERC [321186]
- Region Ile de France
We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x - ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or not, that is, we want to determine the large-time behaviour of the associated solution. This problem has been solved recently when the nonlinearity is of KPP type. We consider in the present paper general reaction terms, that are only assumed to be negative at infinity. Using a variational approach, we construct two thresholds 0 < <(c)under bar> <= (c) over bar < infinity determining the existence and the non-existence of travelling waves. Numerics support the conjecture <(c)under bar> = (c) over bar. We then prove that any solution of the initial-value problem converges at large times, either to 0 or to a travelling wave. In the case of bistable nonlinearities, where the steady state 0 is assumed to be stable, our results lead to constrasting phenomena with respect to the KPP framework. Lastly, we illustrate our results and discuss several open questions through numerics.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据