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math.AP2025
Recovering Initial States in Certain Quasilinear Parabolic Problems from Time Averages
Bogdan-Vasile Matioc, Christoph Walker
The inverse problem of reconstructing the initial state in quasilinear parabolic equations from time averages is investigated. Under suitable regularity assumptions on the quasilin…
math.AP2025
Well-posedness and Rayleigh-Taylor instability of the two-phase periodic quasistationary Stokes flow
Daniel Böhme, Bogdan-Vasile Matioc
We study the two-phase, horizontally periodic, quasistationary Stokes flow in two dimensions driven by surface tension and gravity effects in the general context of fluids with (po…
math.AP2025
A potential theory approach to the capillarity-driven Hele-Shaw problem
Bogdan-Vasile Matioc, Christoph Walker
In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are gover…