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SUMMARY:Scattering for wave equations with sources and slowly decaying dat
 a - Hans Lindblad (Johns Hopkins)
DTSTART:20240429T140000Z
DTEND:20240429T150000Z
UID:TALK215824@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:We construct solutions with prescribed radiation fields for wa
 ve equations with polynomially decaying sources close to the lightcone. In
  this setting\, which is motivated by semilinear wave equations satisfying
  the weak null condition\, solutions to the forward problem have a logarit
 hmic leading order term on the lightcone and non-trivial homogeneous asymp
 totics in the interior of the lightcone. The backward scattering solutions
  we construct from knowledge of the source and the radiation field at null
  infinity alone are given to second order by explicit asymptotic solutions
  which satisfy novel matching conditions close to the light cone. This req
 uires a delicate analysis close to the light cone of the forward solution 
 with sources on the light cone. We also relate the asymptotics of the radi
 ation field towards space-like infinity to explicit homogeneous solutions 
 in the exterior of the light cone for slowly polynomially decaying data co
 rresponding to mass\, charge and angular momentum in the applications. The
  somewhat surprising discovery is that these data can cause the same logar
 ithmic radiation field as the source term. This requires a delicate analys
 is of the forward homogeneous solution close to the light cone using the i
 nvertibility of the Funk transform. This is joint work with Volker Schlue.
LOCATION:MR13
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