16 citations · 61 across the 19 of their papers we have counts for
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On existence, uniqueness and stability of solutions to Cahn-Hilliard/Allen-Cahn systems with cross-kinetic coupling
Aaron Brunk, Herbert Egger, Timileyin David Oyedeji +2
A system of phase-field equations with strong-coupling through state and gradient dependent non-diagonal mobility matrices is studied. Existence of weak solutions is established by…
Existence and weak-strong uniqueness for global weak solutions for the viscoelastic phase separation model in three space dimensions
Aaron Brunk
The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end we apply the relati…
Relative energy and weak-strong uniqueness of the two-phase viscoelastic phase separation model
Aaron Brunk, Maria Lukacova-Medvidova
The aim of this paper is to analyze a viscoelastic phase separation model. We derive a suitable notion of the relative energy taking into account the non-convex nature of the energ…
Existence, regularity and weak-strong uniqueness for the three-dimensional Peterlin viscoelastic model
Aaron Brunk, Yong Lu, Maria Lukacova-Medvidova
In this paper we analyze the three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach we prove the existence of a weak solutions. Further…
Global existence of weak solutions to viscoelastic phase separation: Part II Degenerate Case
Aaron Brunk, Maria Lukacova-Medvidova
The aim of this paper is to prove global in time existence of weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobil…
Global existence of weak solutions to viscoelastic phase separation: Part I Regular Case
Aaron Brunk, Maria Lukacova-Medvidova
We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn-Hilliard-type equation for tw…