Speaker
Description
The relative energy/entropy method has been a powerful tool for establishing (weak-strong) uniqueness, stability, and singular limits in continuum mechanics ever since its inception in the 70s by Dafermos and DiPerna. However, its application to interface evolution problems has faced a major obstacle in the form of the lack of strict convexity of the interface area functional. Recently, it has been shown that this difficulty can be overcome by developing an evolutionary analogue of the concept of calibrations for minimal surfaces. This has enabled the derivation of weak-strong uniqueness principles for curvature-driven evolutions without comparison principle, such as multiphase mean curvature flow or two-phase flow with surface tension, as well as corresponding quantitative convergence results for their diffuse-interface approximations.