Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations

Details Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations

2008-09-11

arxiv.org/abs/0809.2059v3

Mathematics

Dynamical Systems

33 pages, 3 figures; to appear DCDS-A

Scientific paper

We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with unidirectional coupling. This class of lattice equations includes some spatial discretizations for hyperbolic conservation laws with a source term as well as a subclass of monotone systems. We obtain a variational characterization of the critical wave speed above which monotone traveling wave solutions are guaranteed to exist. We also discuss non-monotone waves, and the coexistence of monotone and non-monotone waves.

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