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SUMMARY:A Tale of Two Energies: a Story of Hyperbolic PDEs - Willie WY Won
 g (University of Cambridge)
DTSTART:20101129T170000Z
DTEND:20101129T180000Z
UID:TALK28027@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:To paraphrase Jacques Hadamard: What a partial differential eq
 uation is\, is well known. What hyperbolicity is\, will be explained. I wi
 ll give an expository discussion of systems of partial differential equati
 ons and their local well-posedness\, with focus on the notion of regular h
 yperbolicity due to Demetrios Christodoulou\; in particular the role of en
 ergy estimates will be emphasized and their systematic construction will b
 e described. Within this framework\, a local causal structure of hyperboli
 c equations can be defined\, extending the concept of hyperbolic developme
 nt of Jean Leray. Finally\, I will touch on some recent work in which this
  local causal structure is compared against the background space-time caus
 al structure in the context of Lagrangian theories of maps on a Lorentzian
  manifold.\n\nThe talk will be accessible to non-experts\, and Part III an
 d CCA students are encouraged to attend.\n
LOCATION:CMS\, MR5
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