Existence of traveling waves for vector valued gradient flows

Xinfu Chen; Zhilei Liang

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arXiv · 2506.06647

Existence of traveling waves for vector valued gradient flows

Xinfu Chen·Zhilei Liang

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Abstract

Allen-Cahn equation is a fundamental continuum model that describes phase transitions in multi-component mixtures. We prove the existence of traveling waves for vector valued Allen-Cahn equations in the context of Ginzburg-Landau theories; in addition, we find the largest wave speed and provide its bounds from upper and below. Our method is based on a variation technique and can be applied to system of equations with a gradient flow structure.

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Xinfu Chen, Zhilei Liang. 2025-06-07. Existence of traveling waves for vector valued gradient flows. https://arxiv.org/abs/2506.06647

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