Exponential stabilization of well-posed systems by colocated feedback

Published versio

Structured Perturbations of Semigroup Generators: Theory and Applications

Wir verwenden einen Störungsansatz, um lineare Operatoren und deren Spektral- und Generatoreigenschaften zu untersuchen. Dazu betrachten wir strukturierte Störungen, welche auch im Kontext linearer Systeme mit geschlossenem Feedback betrachtet wurden

Note on basic features of large time behaviour of heat kernels

Large time behaviour of heat semigroups (and more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the general framework of positivity improving selfadjoint semigroups. This framework includes Laplacians on manifolds, metric graphs and discrete graphs.Comment: 24 page