We consider a doubly nonlinear system of porous medium type with a convex and coercive variational integrand in a noncylindrical domain. This talk is split into two parts, where we will distinguish between domains, which are nondecreasing in time, and more general domains, which are also allowed to shrink in time, but are equipped with a one-sided growth condition. Under certain conditions on the domain and the variational integrand, we are able to show in both cases the existence of variational solutions, which are continuous in time, and the existence of the time derivative for the power nonlinearity of the solution in the dual of the given test space.
This is based on a joint work with Leah Schätzler, Christoph Scheven and Jarkko Siltakoski.