Published Paper

Inserted: 9 jan 2024
Last Updated: 16 sep 2025

Journal: Mathematics in Engineering
Volume: 7
Number: 4
Pages: 522-552
Year: 2025
Doi: 10.3934/mine.2025022

Abstract:

We investigate the influence of surfactants on stabilizing the formation of interfaces in solid-solid phase transitions. The analysis focuses on singularly perturbed van der Waals-Cahn-Hillard-type energies for gradient vector fields, supplemented with a term that accounts for the interaction between the surfactant and the solid. Assuming the potential term to have only two rank-one connected wells, we prove that the effective energy for the formation of an interface decreases when the surfactant segregate to the interface.