Dr. K. Stinson (Universität Bonn)
Wednesday, October 26, 2022 - 15:15
Weierstraß-Institut
Mohrenstr. 39, 10117 Berlin, Erhard-Schmidt-Hörsaal, Erdgeschoss
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
The purpose of this talk is to develop a gradient flow perspective for the Mullins--Sekerka equation, intrinsic to the evolving surface, at the level of a weak solution theory. The solution concept is motivated by the De Giorgi framework for curves of maximal slope and consideration of Gamma-convergence for gradient flows in the spirit of Sandier and Serfaty. Solutions must satisfy an optimal energy dissipation relation, where both the time derivative and metric slope are considered with respect to formal tangent spaces, arising from the mass preserving normal velocities. We prove that such solutions exist, may be recast in a PDE sense, and subsume the solution concept introduced by Le in the study of Gamma-convergence for the Cahn--Hilliard equation. As an application, we explore how a related solution concept can be used to understand the sharp interface limit of the Cahn--Hilliard reaction model for phase separation in lithium-ion batteries. Joint works with Sebastian Hensel (U. Bonn) and Tim Laux (U. Bonn).
submitted by eismann (andrea.eismann@wias-berlin.de, 030 20372320)