Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …

Although mathematics ranks last in the Six Arts (rites, music, archery, chariot racing,
calligraphy and mathematics), it is used in the most practical issues and affairs. Maximally, it …

In this paper, the pattern formation of the attraction-repulsion Keller-Segel (ARKS) system is
studied analytically and numerically. By the Hopf bifurcation theorem as well as the local …

We show existence and uniqueness of classical solutions for the motion of immersed
hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a …

THE VOLUME PRESERVING MEAN CURVATURE FLOW NEAR SPHERES 1. Introduction
Let G be a compact, closed, connected, embedded hypersurf Page 1 PROCEEDINGS OF THE …

The Mullins–Sekerka model is a nonlocal evolution model for hypersurfaces, which arises
as a singular limit for the Cahn–Hilliard equation. We show that classical solutions exist …

The Willmore flow leads to a quasilinear evolution equation of fourth order. We study
existence, uniqueness and regularity of solutions. Moreover, we prove that solutions exist …

In this paper we develop a geometric theory for quasilinear parabolic problems in weighted
L p-spaces. We prove existence and uniqueness of solutions as well as the continuous …

Currently the number of reduction methods used in practice in climate applications is vast
and tends to be difficult to access for researchers searching for an overview of the area. In …

We show convergence of solutions to equilibria for quasilinear parabolic evolution
equations in situations where the set of equilibria is non-discrete, but forms a finite …