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Journal article
SPREADING SPEEDS AND TRAVELING WAVES OF NONLOCAL MONOSTABLE EQUATIONS IN TIME AND SPACE PERIODIC HABITATS
Discrete and continuous dynamical systems. Series A, v 35(4), pp 1609-1640
01 Apr 2015
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
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*(., .) and 0 propagating in any given direction of xi with speed c > c* (xi).
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Details
- Title
- SPREADING SPEEDS AND TRAVELING WAVES OF NONLOCAL MONOSTABLE EQUATIONS IN TIME AND SPACE PERIODIC HABITATS
- Creators
- Nar Rawal - Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USAWenxian Shen - Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USAAijun Zhang - Drexel Univ, Dept Math, Philadelphia, PA 19104 USADepartment of Mathematics & Statistics, Auburn University, Auburn, AL 36849Wenjing Shen - Decision Sciences (and Management Information Systems)
- Publication Details
- Discrete and continuous dynamical systems. Series A, v 35(4), pp 1609-1640
- Publisher
- Amer Inst Mathematical Sciences-Aims
- Number of pages
- 32
- Grant note
- DMS-0907752 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Decision Sciences (and Management Information Systems)
- Web of Science ID
- WOS:000346485100013
- Scopus ID
- 2-s2.0-84915756472
- Other Identifier
- 991019173552104721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied