Entropy Formulation of Evolutionary Phase Transitions

The group contributes to the following mathematical research topics of WIAS:

Partial differential equations offer a powerful and versatile framework for the continuum description of phenomena in nature and technology with complex coupling and dependencies. At the Weierstrass Institute this research has three essential focuses: (a) Rigorous mathematical analysis of general evolution equations in terms of existence, uniqueness and regularity of different types of solutions, (b) Development of variational approaches using the toolbox of the calculus of variations, (c) Regularity results for solutions of elliptic and parabolic partial differential equations. [>> more]

Free boundary problems for partial differential equation describe problems such that a partial differential equation is considered on a domain depending on the solution to the equation. [>> more]

A diffuse phase field model is a mathematical model for describing microstructural phenomena and for predicting morphological evolution on the mesoscale. It is applied to a wide variety of material processes such as solidification, coarsening in alloys, crack propagation and martensitic transformations. [>> more]

Many physical phenomena can be described by suitable functionals, whose critical points play the role of equilibrium solutions. Of particular interest are local and global minimizers: a soap bubble minimizes the surface area subject to a given volume and an elastic body minimizes the stored elastic energy subject to given boundary conditions. At WIAS, methids from the calcuus of variations are applied and further developed to solve problems in physics and technology such as continuum mechanics, quantum mechanics, and optimal control. [>> more]