Rocky Mountain Journal of Mathematics

Front-like entire solutionsfor a delayed nonlocal dispersalequation with convolution typebistable nonlinearity

Guo-Bao Zhang and Ruyun Ma

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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.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 4 (2017), 1355-1404.

Dates
First available in Project Euclid: 6 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1501984953

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

Mathematical Reviews number (MathSciNet)
MR3689958

Subjects
Primary: 35K57: Reaction-diffusion equations 35R20: Partial operator-differential equations (i.e., PDE on finite- dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx] 92D25: Population dynamics (general)

Keywords
Nonlocal dispersal entire solutions traveling wavefronts bistable nonlinearity

Citation

Zhang, Guo-Bao; Ma, Ruyun. Front-like entire solutionsfor a delayed nonlocal dispersalequation with convolution typebistable nonlinearity. Rocky Mountain J. Math. 47 (2017), no. 4, 1355--1404. doi:10.1216/RMJ-2017-47-4-1355. https://projecteuclid.org/euclid.rmjm/1501984953


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