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math.AP2026
Surface Stokes-Cahn-Hilliard System: Analysis and Structure-Preserving Discretization
Maxim Olshanskii, Mansur Shakipov
We study the surface Stokes-Cahn-Hilliard system governing tangential flow and phase separation in viscous fluid membranes. The equations are posed on a closed, stationary hy…
math.NA2026
Convergence of a CutFEM for fluid--structure interaction with a deforming interface
Miguel A. Fernández, Buyang Li, Maxim A. Olshanskii
We present a rigorous error analysis for a semidiscrete immersed CutFEM applied to fluid--structure interaction (FSI) problems involving an incompressible viscous fluid and an elas…
math.AP2026
Well-posedness of the heat equation in domains with topological transitions
Maxim Olshanskii, Arnold Reusken
We analyze a linear parabolic equation with homogeneous Dirichlet boundary conditions posed in domains whose evolution may involve topological transitions. The domains are describe…