3 citations · 4 across the 3 of their papers we have counts for
6 papers · 1 filter
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
Harald Garcke, Patrik Knopf, Sourav Mitra +1
In this article, we study the strong well-posedness, stability and optimal control of an incompressible magneto-viscoelastic fluid model in two dimensions. The model consists of an…
Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
Patrik Knopf, Kei Fong Lam, Chun Liu +1
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interacti…
Stratified periodic water waves with singular density gradients
Joachim Escher, Patrik Knopf, Christina Lienstromberg +1
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The f…
Convergence of a Robin boundary approximation for a Cahn--Hilliard system with dynamic boundary conditions
Patrik Knopf, Kei Fong Lam
We prove the existence of unique weak solutions to an extension of a Cahn--Hilliard model proposed recently by C.~Liu and H.~Wu (2019), in which the new dynamic boundary condition…
Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: A gradient flow approach
Harald Garcke, Patrik Knopf
The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of t…
Optimal control of a Vlasov-Poisson plasma by an external magnetic field - The basics for variational calculus
Patrik Knopf
We consider the three dimensional Vlasov-Poisson system that is equipped with an external magnetic field to describe a plasma. The aim of various concrete applications is to contro…