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SUMMARY:Old and new approaches to rate-independent systems - Dr Filip Rind
 ler\, University of Warwick
DTSTART:20150521T130000Z
DTEND:20150521T170000Z
UID:TALK55909@talks.cam.ac.uk
CONTACT:CCA
DESCRIPTION:Many physical systems involve an interplay of elastic (reversi
 ble) and dissipative (irreversible) effects. If the amount of energy that 
 is dissipated (removed from the system) only depends on the traveled dista
 nce in the state space\, but not the rate (speed) by which this movement o
 ccurs\, then the system is called rate-independent. This is almost always 
 only an approximation to reality\, but it turns out to describe a variety 
 of phenomena rather accurately\, among them models of plasticity (permanen
 t deformation) in metals\, shape-memory alloys and damage/fracture in brit
 tle materials - all of which have numerous applications in engineering.\n\
 nMathematically\, these models lead to PDEs with unusual features. Most pr
 ominently\, time derivatives are enclosed in positively $0$-homogeneous fu
 nctions (such as x/|x|)\, whereby we can at most expect BV-regularity in t
 ime. As jumps may really occur in the time-evolution\, we need to specify 
 the behavior of the system over these discontinuities. Many engineering mo
 dels are under-specified in this area and it is up to mathematicians to fi
 nd good concepts of what constitutes solutions.\n\nThis short course will 
 first explain the physical models in some detail and then consider several
  approaches to define mathematical solutions concepts and to "find" corres
 ponding solutions. As this is a vastly unfinished area of mathematical ana
 lysis\, we will end with some future directions and challenges.
LOCATION:MR3
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