Speaker
Description
Several phase-field models have the underlying structure of
generalized gradient systems in Banach spaces, whose evolutions
are generated by the interplay between an energy functional
and a dissipation potential. We focus on the case in which the dual
dissipation potential is given by a sum of two functionals and show
that solutions of the associated gradient-flow evolution equation with
combined dissipation can be constructed by a split-step method, i.e. by
solving alternately the gradient systems featuring only one of the
dissipation potentials and concatenating the corresponding
trajectories. Thereby the construction of solutions is provided either by
semiflows, on the time-continuous level, or by using Alternating Minimizing
Movements in the time-discrete setting. In both cases the convergence
analysis relies on the energy-dissipation principle for gradient systems.
Joint work with Alexander Mielke (Berlin) and Artur Stephan (Vienna).