Prof. Jochen Glück “Convergence results for transition semigroups and applications to parabolic equations with unbounded coefficients”

For a Polish space Ω, we consider an operator semigroup T = (T_t)_{t∈(0,∞)} that acts on the space B_b(Ω) of bounded measurable functions and is given by a family of transition kernels. Building on abstract results from Banach lattice theory we give sufficient conditions for convergence of T_tf (pointwise or uniformly on compact sets) as t → ∞; here, f denotes a bounded measurable function or a bounded continuous function on Ω.

Finally we show how these convergence results can be applied to analyse the long-term behaviour of the solutions to parabolic PDEs on R^d with unbounded coefficients.

The talk is based on joint work with Moritz Gerlach and Markus Kunze.