Second order parabolic equations with non-local boundary conditions on L∞(Ω) and C(Ω̅): generation, regularity and asymptotics

Erstveröffentlichung
2017-07-05Authors
Kunkel, Stefan
Referee
Arendt, WolfgangZacher, Rico
Dissertation
Faculties
Fakultät für Mathematik und WirtschaftswissenschaftenInstitutions
Institut für Angewandte AnalysisAbstract
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 for its solutions we will prove regularity results as well as give results on the
asymptotic behavior as t → ∞ . One of our main arguments is the transference of properties of the equation with local boundary conditions to the one with non-local boundary conditions. Great care will be
taken to ensure that we do not need more regularity assumptions on Ω and on the coefficients of differential operator compared to the best known local results.
Date created
2016
Subject headings
[GND]: Evolutionsgleichung | Randbedingung <Mathematik> | Dirichlet-Randbedingung | Robin-Randwertproblem | Asymptotik | Feller-Prozess[LCSH]: Evolution equations | Boundary value problems
[Free subject headings]: Non-local boundary conditions | Dirichlet boundary conditions | Robin boundary conditions | Asymptotics | Strong Feller property | Operator semigroups | Evolutionary equations
[DDC subject group]: DDC 510 / Mathematics
Metadata
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Please use this identifier to cite or link to this item: http://dx.doi.org/10.18725/OPARU-4416
Kunkel, Stefan (2017): Second order parabolic equations with non-local boundary conditions on L∞(Ω) and C(Ω̅): generation, regularity and asymptotics. Open Access Repositorium der Universität Ulm und Technischen Hochschule Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-4416
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