Entire solutions with merging fronts to a bistable periodic lattice dynamical system

Shi-Liang Wu; Cheng-Hsiung Hsu

doi:10.3934/dcds.2016.36.2329

Article Contents

2016, Volume 36, Issue 4: 2329-2346. Doi: 10.3934/dcds.2016.36.2329

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Entire solutions with merging fronts to a bistable periodic lattice dynamical system

Shi-Liang Wu^1, and
Cheng-Hsiung Hsu^2,

1.
Department of Mathematics, Xidian University, Xi’an, Shaanxi 710071
2.
Department of Mathematics, National Central University, Chung-Li 32001

Received: August 31, 2014

Revised: June 30, 2015

Published: May 2017

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Abstract

We are interested in finding entire solutions of a bistable periodic lattice dynamical system. By constructing appropriate super- and subsolutions of the system, we establish two different types of merging-front entire solutions. The first type can be characterized by two monostable fronts merging and converging to a single bistable front; while the second type is a solution which behaves as a monostable front merging with a bistable front and one chases another from the same side of $x$-axis. For this discrete and spatially periodic system, we have to emphasize that there has no symmetry between the increasing and decreasing pulsating traveling fronts, which increases the difficulty of construction of the super- and subsolutions.

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Mathematics Subject Classification: Primary: 35K57, 34A34, 34E05; Secondary: 92D25, 92D30.

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