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Invariant sets and long time behaviour of operator semigroups
(Universität Ulm, 2017-02-10)
In this PhD thesis, strongly continuous operator semigroups are studied. We show that contractivity or positivity of such a semigroup can have a profound impact on its long time behaviour. Moreover, we perform a detailed ...
The principle of linearised stability for non-linear parabolic Volterra equations
(Universität Ulm, 2018-07-12)
This thesis is concerned with the long-time behaviour of solutions to non-linear abstract parabolic Volterra equations. The focus is both on a wide class of semilinear parabolic Volterra equations and on quasilinear ...
Second order parabolic equations with non-local boundary conditions on L∞(Ω) and C(Ω̅): generation, regularity and asymptotics
(Universität Ulm, 2017-07-05)
The aim of the present thesis is to analyze second order parabolic equations with non-local boundary conditions of Dirichlet and Robin type on the spaces L∞(Ω) and C(Ω̅). We will prove well-posedness of such equations and ...
Vector-valued elliptic boundary value problems on rough domains
(Universität Ulm, 2019-02-07)
In this thesis we study elliptic boundary value problems in the setting of vector-valued functions on arbitrary open and bounded sets. The first part considers Sobolev spaces of vector-valued functions, in particular mapping ...