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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Scattering for wave equations with sources and slo
wly decaying data - Hans Lindblad (Johns Hopkins)
DTSTART;TZID=Europe/London:20240429T150000
DTEND;TZID=Europe/London:20240429T160000
UID:TALK215824AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/215824
DESCRIPTION:We construct solutions with prescribed radiation f
ields for wave equations with polynomially decayin
g 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 logarithmic leading ord
er term on the lightcone and non-trivial homogeneo
us asymptotics in the interior of the lightcone. T
he backward scattering solutions we construct from
knowledge of the source and the radiation field a
t null infinity alone are given to second order by
explicit asymptotic solutions which satisfy novel
matching conditions close to the light cone. This
requires a delicate analysis close to the light c
one of the forward solution with sources on the li
ght cone. We also relate the asymptotics of the ra
diation field towards space-like infinity to expli
cit homogeneous solutions in the exterior of the l
ight cone for slowly polynomially decaying data co
rresponding to mass\, charge and angular momentum
in the applications. The somewhat surprising disco
very is that these data can cause the same logarit
hmic radiation field as the source term. This requ
ires a delicate analysis of the forward homogeneou
s solution close to the light cone using the inver
tibility of the Funk transform. This is joint work
with Volker Schlue.
LOCATION:MR13
CONTACT:Dr Greg Taujanskas
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