Spreading Speeds and Traveling Waves of Nonlocal Monostable Equations in Time and Space Periodic Habitats
By Nar Rawal, Wenxian Shen, Aijun Zhang. 2013
64 citations recorded by the source corpus.
This paper is devoted to the investigation of spatial spreading speeds and traveling wave solutions of monostable evolution equations with nonlocal dispersal in time and space periodic habitats. It has been shown in an earlier work by the first two authors of the current paper that such an equation has a unique time and space periodic positive stable solution $u^*(t,x)$. In this paper, we show that such an equation has a spatial spreading speed $c^*(\xi)$ in the direction of any given unit vector $\xi$. A variational characterization of $c^*(\xi)$ is given. Under the assumption that the nonlocal dispersal operator associated to the linearization of the monostable equation at the trivial solution $0$ has a principal eigenvalue, we also show that the monostable equation has a continuous periodic traveling wave solution connecting $u^*(\cdot,\cdot)$ and $0$ propagating in any given direction of $\xi$ with speed $c>c^*(\xi)$.
Subfields: Applied Mathematics, Control and Systems Engineering, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/4f5083885da53f5073127c6e3b47b3ef56dba445
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In Applied Mathematics
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Citations in the corpus
- Approximations of random dispersal operators/equations by nonlocal dispersal operators/equations (2014, background): “ons of various dynamics of random dispersal evolution equations by those of nonlocal dispersal evolution equations. We also remark that some necessary and sufficient conditions are provided in [36] and [37] for λδ(a) to be the principal eigenvalue of (1.11). Among other, it is proved in [36, Theorem A”
- Traveling waves and spreading speeds for time-space periodic monotone systems (2015, background): “Most recently, Rawal, Shen and Zhang [32] introduced the following definition of time-space periodic traveling waves for a nonlocal dispersal Fisher-KPP equation: Definition 1.2.”