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CATEGORIES:Geometric Analysis &amp\; Partial Differential Equ
 ations seminar
SUMMARY:A Tale of Two Energies: a Story of Hyperbolic PDEs
  - Willie WY Wong (University of Cambridge)
DTSTART;TZID=Europe/London:20101129T170000
DTEND;TZID=Europe/London:20101129T180000
UID:TALK28027AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28027
DESCRIPTION:To paraphrase Jacques Hadamard: What a partial dif
 ferential equation is\, is well known. What hyperb
 olicity is\, will be explained. I will give an exp
 ository discussion of systems of partial different
 ial equations and their local well-posedness\, wit
 h focus on the notion of regular hyperbolicity due
  to Demetrios Christodoulou\; in particular the ro
 le of energy estimates will be emphasized and thei
 r systematic construction will be described. Withi
 n this framework\, a local causal structure of hyp
 erbolic equations can be defined\, extending the c
 oncept of hyperbolic development of Jean Leray. Fi
 nally\, I will touch on some recent work in which 
 this local causal structure is compared against th
 e background space-time causal structure in the co
 ntext of Lagrangian theories of maps on a Lorentzi
 an manifold.\n\nThe talk will be accessible to non
 -experts\, and Part III and CCA students are encou
 raged to attend.\n
LOCATION:CMS\, MR5
CONTACT:Prof. Mihalis Dafermos
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