7 papers
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…
Linearized Stability of Non-Isolated Equilibria of Quasilinear Parabolic Problems in Interpolation Spaces
Bogdan-Vasile Matioc, Christoph Walker
The stability of non-isolated equilibria to quasilinear parabolic problems of the form is established in interpolation spaces (and thus extending previous resul…
The -dimensional gravity driven Muskat problem
Bogdan-Vasile Matioc, Georg Prokert
We study the Muskat problem, which describes the motion of two immiscible, incompressible fluids in a homogeneous porous medium occupying the full space , $N \g…
On the principle of linearized stability for quasilinear evolution equations in time-weighted spaces
Bogdan-Vasile Matioc, Lina Sophie Schmitz, Christoph Walker
Quasilinear (and semilinear) parabolic problems of the form with strict inclusion of the domains of the function $v\maps…
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…
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…