Competing interactions and traveling wave solutions in lattice differential equations

E. S. Van Vleck; Aijun  Zhang

doi:10.3934/cpaa.2016.15.457

Article Contents

2016, Volume 15, Issue 2: 457-475. Doi: 10.3934/cpaa.2016.15.457

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Competing interactions and traveling wave solutions in lattice differential equations

E. S. Van Vleck^1, and
Aijun Zhang^2,

1.
Department of Mathematics, University of Kansas, Lawrence, KS 66045
2.
Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701

Received: March 2015

Revised: November 2015

Published: March 2016

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Abstract

The existence of traveling front solutions to bistable lattice differential equations in the absence of a comparison principle is studied. The results are in the spirit of those in Bates, Chen, and Chmaj [1], but are applicable to vector equations and to more general limiting systems. An abstract result on the persistence of traveling wave solutions is obtained and is then applied to lattice differential equations with repelling first and/or second neighbor interactions and to some problems with infinite range interactions.

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Mathematics Subject Classification: Primary: 39A12, 34K31, 35K57, 37L60.

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References

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