MR14 - Centre for Mathematical Sciences
Cambridge, United Kingdom
Thursday, 21 May 2015
from 14:00 to 18:00
Dr Filip Rindler
University of Warwick
Mathematically, these models lead to PDEs with unusual features. Most prominently, time derivatives are enclosed in positively $0$-homogeneous functions (such as x/|x|), whereby we can at most expect BV-regularity in time. As jumps may really occur in the time-evolution, we need to specify the behavior of the system over these discontinuities. Many engineering models are under-specified in this area and it is up to mathematicians to find good concepts of what constitutes solutions.
This short course will first explain the physical models in some detail and then consider several approaches to define mathematical solutions concepts and to “find” corresponding solutions. As this is a vastly unfinished area of mathematical analysis, we will end with some future directions and challenges.