Semigroups Generated by Multivalued Operators and Domain Convergence for Parabolic Problems
摘要
The following version of the Lumer–Phillips Theorem is proved: a surjective dissipative operator is m-dissipative and invertible. This result remains true if dissipative linear relations (i.e. multivalued operators) are considered. The main purpose of this article is to study relations which generate semigroups. We consider m-dissipative relations and also the holomorphic estimate for relations. Such relations are very useful if domain perturbations for the Laplacian are studied.