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SUMMARY:Well-posedness of weakly hyperbolic systems of PDEs in Gevrey regu
 larity. - Baptiste Morisse\, University of Cardiff
DTSTART:20180212T150000Z
DTEND:20180212T160000Z
UID:TALK98965@talks.cam.ac.uk
CONTACT:Josephine Evans
DESCRIPTION:I consider systems of first-order PDEs\, which are weakly hype
 rbolic: the spectrum of the principal symbol is real but eigenvalues may c
 ross. Close to one of those crossing eigenvalues\,  lower order linear ter
 ms may induce a typical Gevrey growth in frequency. I will present an ener
 gy estimate in Gevrey regularity\, using an approximate symmetrizer of the
  principal symbol. The symbol of such an approximate symmetrizer is in a s
 pecial class of symbols\, related to a specific metric in phase space. For
  such symbols\, composition of associated operators lead to error terms th
 at only can be handle thanks to the Gevrey energy.\n\n 
LOCATION:CMS\, MR13
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