Stability of the stationary profiles of the Allen-Cahn equation with not constant stiffness (original) (raw)

2020, arXiv: Pattern Formation and Solitons

Abstract

We study the solutions of a generalized Allen-Cahn equation deduced from a Landau energy functional, endowed with a non-constant higher order stiffness. We assume the stiffness to be a positive function of the field and we discuss the stability of the stationary solutions proving both linear and local non-linear stability.

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