Degenerate diffusion - behaviour at the boundary and kernel estimates

Veröffentlichung
2010-06-29
Dissertation
Authors
Chovanec, Michal
Faculties
Fakultät für Mathematik und WirtschaftswissenschaftenAbstract
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
WohlgestelltheitDewey Decimal Group
DDC 510 / MathematicsMetadata
Show full item recordCitation example
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