62 citations · 396 across the 27 of their papers we have counts for
28 papers
The anisotropic Cahn--Hilliard equation with degenerate mobility: Existence of weak solutions
Harald Garcke, Patrik Knopf, Andrea Signori
This paper presents an existence result for the anisotropic Cahn--Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account a…
Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions
Patrik Knopf, Jonas Stange
We consider a general class of bulk-surface convective Cahn--Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic bo…
Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions
Pierluigi Colli, Patrik Knopf, Giulio Schimperna +1
We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium.…
The anisotropic Cahn--Hilliard equation: regularity theory and strict separation properties
Harald Garcke, Patrik Knopf, Julia Wittmann
The Cahn--Hilliard equation with anisotropic energy contributions frequently appears in many physical systems. Systematic analytical results for the case with the relevant logarith…
Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures
Harald Garcke, Paul Hüttl, Christian Kahle +1
We consider an optimization problem for the eigenvalues of a multi-material elastic structure that was previously introduced by Garcke et al. [Adv. Nonlinear Anal. 11 (2022), no. 1…
Controlling a Vlasov-Poisson plasma by a Particle-In-Cell method based on a Monte Carlo framework
Jan Bartsch, Patrik Knopf, Stefania Scheurer +1
The Vlasov-Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an ex…