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UID:7da862c8c2894fff7712a62d111ca33d
CATEGORIES:Hyperbolic & Dispersive PDE Seminar
CREATED:20230417T195925
SUMMARY:Scattering for wave equations with sources and slowly decaying data. 
LOCATION:705
DESCRIPTION:<div style="border: 0px; font-style: normal; font-weight: 400; font-size: 1
 6px; line-height: inherit; font-family: Calibri, Arial, Helvetica, sans-ser
 if; margin: 0px; padding: 0px; vertical-align: baseline; color: #000000; le
 tter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text
 -transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Abstr
 act:&nbsp;&nbsp;</div><div style="border: 0px; font-style: normal; font-wei
 ght: 400; font-size: 16px; line-height: inherit; font-family: Calibri, Aria
 l, Helvetica, sans-serif; margin: 0px; padding: 0px; vertical-align: baseli
 ne; color: #000000; letter-spacing: normal; orphans: 2; text-align: start; 
 text-indent: 0px; text-transform: none; white-space: normal; widows: 2; wor
 d-spacing: 0px;">We construct &nbsp;solutions with prescribed radiation fie
 lds for wave equations with polynomially decaying sources close to the ligh
 tcone. In this setting, which is motivated by semi-linear wave equations sa
 tisfying the weak null condition, solutions to the forward problem have a l
 ogarithmic leading order term on the lightcone and non-trivial homogeneous 
 asymptotics in the interior of the lightcone. The backward scattering solut
 ions we construct from knowledge of the source and the radiation field at n
 ull infinity alone are given to second order &nbsp;by explicit asymptotic s
 olutions which satisfy novel matching conditions close to the light cone. W
 e also relate the asymptotics of the radiation field towards space-like inf
 inity to explicit &nbsp;homogeneous solutions in the exterior of the light 
 cone for slowly polynomially decaying data corresponding to mass, charge an
 d angular momentum in the applications. The somewhat surprising discovery i
 s that these data can cause the same logarithmic radiation field as the sou
 rce term. This requires a delicate analysis of the forward homogeneous solu
 tion close to the light cone using the invertibility of the Funk transform.
 </div><div style="border: 0px; font-style: normal; font-weight: 400; font-s
 ize: 16px; line-height: inherit; font-family: Calibri, Arial, Helvetica, sa
 ns-serif; margin: 0px; padding: 0px; vertical-align: baseline; color: #0000
 00; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px
 ; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"
 >This is joint work with Volker Schlue.&nbsp;</div>
CONTACT:Hans Lindblad
DTSTAMP:20260828T123208
DTSTART;TZID=America/New_York:20230420T153000
DTEND;TZID=America/New_York:20230420T163000
SEQUENCE:0
TRANSP:OPAQUE
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