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2004 Fronts on a lattice
Lambertus A. Peletier, José Antonio Rodríguez
Differential Integral Equations 17(9-10): 1013-1042 (2004).

Abstract

Motivated by a model of a system of many particles at low densities, we consider a lattice differential equation with two uniform steady states and we investigate the existence of travelling fronts connecting them. This leads to a two-point boundary-value problem for a nonlinear delay-differential equation. We replace the original parabolic nonlinearity by a piecewise-linear function, where explicit computations are possible. We find monotone and nonmonotone fronts. Finally we also describe all the fronts such that the $\alpha$-limit is the unstable uniform state. For different values of the wave speed $c$ of the front we find bounded and unbounded as well as eventually periodic orbits, i.e., orbits $u_c (x)$ that are periodic for $x\geqslant x_{\text{per}}(c)$ for some $x_{\text{per}}(c)\in{{\mathbb {R}}}$.

Citation

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Lambertus A. Peletier. José Antonio Rodríguez. "Fronts on a lattice." Differential Integral Equations 17 (9-10) 1013 - 1042, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1150.34448
MathSciNet: MR2082458

Subjects:
Primary: 37L60
Secondary: 34C37, 82C32

Rights: Copyright © 2004 Khayyam Publishing, Inc.

JOURNAL ARTICLE
30 PAGES


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Vol.17 • No. 9-10 • 2004
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