20 citations · 24 across the 7 of their papers we have counts for
10 papers
Sharp Convergence to the Half-Space for Mullins-Sekerka in the Plane
Wenhui Shi, Maria G. Westdickenberg, Michael Westdickenberg
We revisit the HED Method for the Mullins-Sekerka evolution in the plane. We identify a natural notion of distance, intrinsic to the interface itself. Using this distance, the ener…
Optimal relaxation of bump-like solutions of the one-dimensional Cahn-Hilliard equation
Sarah Biesenbach, Richard Schubert, Maria G. Westdickenberg
REVISED VERSION INCORPORATING THE ERRATUM ON LEMMA 2.1 AND WITH A CORRECTION TO LEMMA 2.8 In this paper we derive optimal relaxation rates for the Cahn-Hilliard equation on the one…
Numerics and analysis of Cahn--Hilliard critical points
Tobias Grafke, Sebastian Scholtes, Alfred Wagner +1
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in and the critical parameter regime of large system…
Symmetry of constrained minimizers of the Cahn-Hilliard energy on the torus
Michael Gelantalis, Alfred Wagner, Maria G. Westdickenberg
We establish sufficient conditions for a function on the torus to be equal to its Steiner symmetrization and apply the result to volume-constrained minimizers of the Cahn-Hilliard…
Optimal -type relaxation rates for the Cahn-Hilliard equation on the line
Felix Otto, Sebastian Scholtes, Maria G. Westdickenberg
In this paper we derive optimal algebraic-in-time relaxation rates to the kink for the Cahn-Hilliard equation on the line. We assume that the initial data have a finite distance---…
Optimal relaxation to a planar interface in the Mullins-Sekerka problem
Olga Chugreeva, Felix Otto, Maria G. Westdickenberg
We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation.…
Metastability of the Cahn-Hilliard equation in one space dimension
Sebastian Scholtes, Maria G. Westdickenberg
We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in away from a point on the so-ca…
Existence and properties of certain critical points of the Cahn-Hilliard energy
Michael Gelantalis, Alfred Wagner, Maria G. Westdickenberg
The Cahn-Hilliard energy landscape on the torus is explored in the critical regime of large system size and mean value close to . Existence and properties of a "droplet-shaped"…
Energy barrier and -convergence in the -dimensional Cahn-Hilliard equation
Michael Gelantalis, Maria G. Westdickenberg
We study the d-dimensional Cahn-Hilliard equation on the flat torus in a parameter regime in which the system size is large and the mean value is close---but not too close---to -1.…
Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size
Felix Otto, Hendrik Weber, Maria Westdickenberg
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneou…