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Degenerate diffusion - behaviour at the boundary and kernel estimates

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122 Seiten
 
Veröffentlichung
2010-06-29
DOI
10.18725/OPARU-1791
Dissertation


Authors
Chovanec, Michal
Faculties
Fakultät für Mathematik und Wirtschaftswissenschaften
License
Standard (Fassung vom 01.10.2008)
https://oparu.uni-ulm.de/xmlui/license_v2
Abstract
We study evolution equations of the form: \begin{equation*} \frac{\partial u}{\partial t}(t,x)=m(x)(\triangle u)(t,x)\qquad t\in\R_+,\,x\in\Omega, \end{equation*} where $\Omega$ is a bounded domain in $\R^N$ and the function $m:\Omega\rightarrow (0,\infty)$ is assumed to be measurable. Dirichlet boundary conditions are posed. We investigate under which conditions on $m$ and $\partial\Omega$ the operator $m\triangle$ generates a strongly continuous semigroup on $C_0(\Omega)$. In the second part of the thesis we obtain various estimates on the kernel of the semigroup generated by $m\triangle$ on weighted $L^p$-spaces.
Date created
2010
Subject Headings
Eigenfunktion [GND]
Evolutionsgleichung [GND]
Korrekt gestelltes Problem [GND]
Randverhalten [GND]
Boundary value problems [LCSH]
Evolution equations [LCSH]
Keywords
Wohlgestelltheit
Dewey Decimal Group
DDC 510 / Mathematics

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Chovanec, Michal (2010): Degenerate diffusion - behaviour at the boundary and kernel estimates. Open Access Repositorium der Universität Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-1791

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