Mother Operators and their Descendants
Analysis of PDEs
2014-01-23 v6
Abstract
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be generated by this abstract mechanism using suitable projections. The complexity of the dynamics of the phenomena considered can be described in terms of suitable material laws. The idea is illustrated with a number of concrete examples.
Cite
@article{arxiv.1203.6762,
title = {Mother Operators and their Descendants},
author = {Rainer Picard and Sascha Trostorff and Marcus Waurick},
journal= {arXiv preprint arXiv:1203.6762},
year = {2014}
}
Comments
This is a revised version of the earlier posted pre-print. The corrections concern predominantly Corollary 1.7 and Theorem 1.9 and their consequences