Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats
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- by Wenxian Shen and Aijun Zhang PDF
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Abstract:
This paper deals with positive stationary solutions and spreading speeds of monostable equations with nonlocal dispersal in spatially periodic habitats. The existence and uniqueness of positive stationary solutions and the existence and characterization of spreading speeds of such equations with symmetric convolution kernels are established in the authors’ earlier work for the following cases: the nonlocal dispersal is nearly local; the periodic habitat is nearly globally homogeneous or it is nearly homogeneous in a region where it is most conducive to population growth. The above conditions guarantee the existence of principal eigenvalues of nonlocal dispersal operators associated to linearized equations at the trivial solution. In general, a nonlocal dispersal operator may not have a principal eigenvalue. In this paper, we extend our earlier results to general spatially periodic nonlocal monostable equations. As a consequence, it is seen that the spatial spreading feature is generic for monostable equations with nonlocal dispersal.References
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Additional Information
- Wenxian Shen
- Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
- MR Author ID: 249920
- Email: wenxish@auburn.edu
- Aijun Zhang
- Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
- Email: zhangai@auburn.edu
- Received by editor(s): September 17, 2010
- Received by editor(s) in revised form: January 17, 2011
- Published electronically: September 2, 2011
- Additional Notes: This work was partially supported by NSF grant DMS–0907752
- Communicated by: Yingfei Yi
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1681-1696
- MSC (2010): Primary 45C05, 45G10, 45M20, 47G10, 92D25
- DOI: https://doi.org/10.1090/S0002-9939-2011-11011-6
- MathSciNet review: 2869152