The amplitude equation for weakly nonlinear reversible phase boundaries

2015/10/02 by Jean-François Coulombel, Coulombel, Jean-François, Sylvie Benzoni-Gavage +1
Computer Science · Earth and Planetary Sciences · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.1510.00540

openalex publication_date 2015/10/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This technical note is a complement to an earlier paper [Benzoni-Gavage & Rosini, Comput. Math. Appl. 2009], which aims at a deeper understanding of a basic model for propagating phase boundaries that was proved to admit surface waves [Benzoni-Gavage, Nonlinear Anal. 1998]. The amplitude equation governing the evolution of weakly nonlinear surface waves for that model is computed explicitly, and is eventually found to have enough symmetry properties for the associated Cauchy problem to be locally well-posed.

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