Title
Eulerian vs. Lagrangian: Boundary interaction problems, injectivity and
convergence on changing domains
Abstract
In continuum mechanics there has always been a dichotomy between the
Lagrangian and Eulerian description. The former tries to describe the
problem in terms of a fixed reference configuration while the latter
tries to do the same in the actual physical coordinates. Formally these
are equivalent, yet mathematically their individual usefulness strongly
depends on the specific problem. This is fine until one considers
coupled problems, where neither can be used well on its own. Then
suddenly what seems a boring applied problem requires non-trivial pure
analysis, dealing with strict injectivity requirements, nonlinear
boundary conditions and even function spaces that itself depend on other
parts of the solution.
The aim of this talk is to give an overview of some of the issues that
arise in some examples from continuum mechanics, how some of them
directly motivate abstract theory, how to work on changing domains and
how sometimes, without injectivity, it is not even possible to define
solutions to the problem in the first place.
