The decay rates of Traveling Waves for a class of Nonlocal Evolution Equations

TL;DR

This paper determines the exact decay rates of traveling waves in certain nonlocal evolution equations related to phase transitions and analyzes the spectrum of the linearized operator at these waves.

Contribution

It provides the first precise decay rates for traveling waves and a detailed spectral analysis of the linearized operator in this class of nonlocal equations.

Findings

Exact decay rates of traveling waves are established.

Spectrum of the linearized operator is fully characterized.

Results advance understanding of phase transition models.

Abstract

We obtain the precise decay rates of traveling wave for a class of nonlocal evolution equations arising in the theory of phase transitions. We also investigate the spectrum of the operator obtained by linearizing at such a traveling wave. The detailed description of the spectrum is established.