Weak and strong approximation of semigroups on Hilbert spaces. (English) Zbl 1387.35049
Summary: For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators, in the weak operator topology, in the strong operator topology or in certain integral norms are equivalent under certain natural assumptions which are frequently met in applications.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 47D03 | Groups and semigroups of linear operators |
| 47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
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