On Non-Autonomous Evolutionary Problems
Analysis of PDEs
2013-02-07 v1 Functional Analysis
Abstract
The paper extends well-posedness results of a previously explored class of time-shift invariant evolutionary problems to the case of non-autonomous media. The Hilbert space setting developed for the time-shift invariant case can be utilized to obtain an elementary approach to non-autonomous equations. The results cover a large class of evolutionary equations, where well-known strategies like evolution families may be difficult to use or fail to work. We exemplify the approach with an application to a Kelvin-Voigt-type model for visco-elastic solids.
Cite
@article{arxiv.1302.1304,
title = {On Non-Autonomous Evolutionary Problems},
author = {Rainer Picard and Sascha Trostorff and Marcus Waurick and Maria Wehowski},
journal= {arXiv preprint arXiv:1302.1304},
year = {2013}
}
Comments
31 pages