Department of Mathematics
Title : Invariance of Convex Sets for Evolution Equations
| Speaker: Prof. Wolfgang Arendt Affiliation: University of Ulm Time: 11:00 am Thursday, 21 March, 2013 Location: Room 412 (Building 303) |
Abstract
| Given a system of differential equations it is of great interest to determine whether a closed convex set is invariant by the solutions; i.e., if the inititial value is in the set then the solution remains in the set forever. For example, if one studies dynamical systems coming form populations dynamics or reactions diffusion equations it is of great value to have this invariance property. In the talk we will consider linear initial value problems in Hilbert space. A famous criterion of Beurling-Deny characterizes invariance of a positive cone if the equation is governed by a form. We extend this criterion to non-autonomous equations and also to arbitrary convex sets instead of cones. The talk is based on a recent paper joint with Dominik Dier and El Maati Ouhabaz (arXiv 2013). |
-
Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
