Math.Koll. am 23.05.07/Prof. Juengel
Institut für Mathematik
sekr.mathematik at univie.ac.at
Fri May 18 10:11:02 CEST 2007
Prof. Ansgar Juengel (Universitaet Mainz, Institut fuer Mathematik)
mit dem Thema: ''An algorithmic construction of a priori estimates for
nonlinear higher-order PDEs''
The proof of analytical and numerical properties of solutions to nonlinear
evolution equations is usually based on appropriate a priori estimates and
monotonicity properties of Lyapunov functionals, which are called here
entropies. These estimates can be shown by subtle integration by parts.
However, such proofs are usually skillful and not systematic. In this talk a
systematic method for the derivation of a priori estimates for a large class
of nonlinear evolution equations of higher order in one and several
variables with periodic boundary conditions is presented. This class of
equations contains, for instance, the porous medium equation, the thin-film
equation, and a semiconductor quantum fluid model.
The main idea is the identification of the integrations by parts with
polynomial manipulations. The proof of a priori estimates is then formally
equivalent to the solution of a decision problem known in real algebraic
geometry, which can be solved algorithmically. The method also allows to
prove decay rates of the solutions to their equilibrium and to derive new
logarithmic Sobolev inequalities.
Zeit: Mittwoch, 23. Mai 2007, 15.45 Uhr (Kaffeejause), anschließend 16.15
Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
Seminarraum C 2.09
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