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Stability analysis for stationary solutions of the Mullins–Sekerka flow with boundary contact

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  • Harald Garcke
  • Maximilian Rauchecker

Abstract

We first give a complete linearized stability analysis around stationary solutions of the Mullins–Sekerka flow with 90° contact angle in two space dimensions. The stationary solutions include flat interfaces, as well as arcs of circles. We investigate the different stability behaviour in dependence of properties of the stationary solution, such as its curvature and length, as well as the curvature of the boundary of the domain at the two contact points. We show that the behaviour changes in terms of these parameters, ranging from exponential stability to instability. We also give a first result on nonlinear stability for curved boundaries.

Suggested Citation

  • Harald Garcke & Maximilian Rauchecker, 2022. "Stability analysis for stationary solutions of the Mullins–Sekerka flow with boundary contact," Mathematische Nachrichten, Wiley Blackwell, vol. 295(4), pages 683-705, April.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:4:p:683-705
    DOI: 10.1002/mana.201900303
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