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UID:20251028T151902EDT-4742AZo3UV@132.216.98.100
DTSTAMP:20251028T191902Z
DESCRIPTION:Title: Reflection coefficient of a fractional reflector\n\n \n
 \nAbstract: In seismology and in oil exploration\, the diffraction or refr
 action of sound by an interface where there is a jump of sound velocity\, 
 formulae are well known. However\, little is known when the velocity is co
 ntinuous and has a jump in one of its derivatives (even a fractional one)
 \n\nThis talk defines and give an estimate for the reflection $R$ coeffici
 ent for solutions of the Helmholtz equation (\Delta u -c^{-2}(1+l(((x_{1})
 _+^{\alpha}))\partial^2_{t^2}u=0 that is $e^{-i\omega t+ ik_2x_2+i\sqrt{\f
 rac{\omega^2}{c^2}-k_2^2}x_1}+R.e^{-i\omega t+ ik_2x_2-i\sqrt{\frac{\omega
 ^2}{c^2}-k_2^2}x_1}$ for $x_1<0$ and $Tu^{>}$ for $x_1>0$.\n\nThis passes 
 through the precise definition of an 'outgoing at infinity wave' u^{>} and
  its precise expression\, using the limiting absorption principle. The lea
 ding order term of R is a Fourier multiplier\, whose principal symbol will
  be given.\n\n \n\nZoom link: https://umontreal.zoom.us/j/83118539851?pwd=
 bk5IOXBLNDRNSnR4dEcrSUFJVWhPZz09\n\nMeeting ID: 831 1853 9851\n\nPasscode:
  215516\n\n \n
DTSTART:20230217T193000Z
DTEND:20230217T203000Z
SUMMARY:Olivier Lafitte (Institut Galilée\, Université Paris 13)
URL:/mathstat/channels/event/olivier-lafitte-institut-
 galilee-universite-paris-13-346059
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