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2017 Front-like entire solutionsfor a delayed nonlocal dispersalequation with convolution typebistable nonlinearity
Guo-Bao Zhang, Ruyun Ma
Rocky Mountain J. Math. 47(4): 1355-1404 (2017). DOI: 10.1216/RMJ-2017-47-4-1355

Abstract

This paper is concerned with front-like entire solutions of a delayed nonlocal dispersal equation with convolution type bistable nonlinearity. Here, a solution defined for all $(x, t)\in \mathbb {R}^2$ is an entire solution. It is known that the equation has an increasing traveling wavefront with nonzero wave speed under some reasonable conditions. We first give the asymptotic behavior of traveling wavefronts at infinity. Then, by the comparison argument and sub-super-solutions method, we construct new types of entire solutions other than traveling wavefronts and equilibrium solutions of the equation, which behave like two increasing traveling wavefronts propagating from both sides of the $x$-axis and annihilate at a finite time. Finally, various qualitative properties of the entire solutions are also investigated.

Citation

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Guo-Bao Zhang. Ruyun Ma. "Front-like entire solutionsfor a delayed nonlocal dispersalequation with convolution typebistable nonlinearity." Rocky Mountain J. Math. 47 (4) 1355 - 1404, 2017. https://doi.org/10.1216/RMJ-2017-47-4-1355

Information

Published: 2017
First available in Project Euclid: 6 August 2017

MathSciNet: MR3689958
Digital Object Identifier: 10.1216/RMJ-2017-47-4-1355

Subjects:
Primary: 35K57, 35R20, 92D25

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 4 • 2017
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