On a visco-elastic Mullins-Sekerka System

Helmut Abels; Harald Garcke; Jonas Haselböck

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arXiv · 2608.19999

On a visco-elastic Mullins-Sekerka System

Helmut Abels·Harald Garcke·Jonas Haselböck

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Abstract

We introduce a novel visco-elastic Mullins-Sekerka system with a prescribed constant contact angle at the boundary. The system is derived as an $H^{-1}$-$H^1$-type gradient flow of an energy consisting of the perimeter together with capillary, elastic, and second-gradient contributions. Building on the framework of Hensel and Stinson (Arch. Ration. Mech. Anal. 248, 2024), we introduce a measure-valued solution concept featuring a sharp De Giorgi-type energy-dissipation inequality. Moreover, we establish existence of solutions via an implicit time discretization scheme, and prove existence of $BV$ solutions under an energy-conservation hypothesis.

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Helmut Abels, Harald Garcke, Jonas Haselböck. 2026-08-20. On a visco-elastic Mullins-Sekerka System. https://arxiv.org/abs/2608.19999

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