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SUMMARY:Damped wave equation with unbounded damping
DTSTART:20231002T120000Z
DTEND:20231002T130000Z
DTSTAMP:20260610T161500Z
UID:indico-event-10296@indico.math.cnrs.fr
DESCRIPTION:Speakers: Petr Siegl (TU Graz)\n\nWe present main ideas in the
  spectral and pseudospectral analysis of the damped wave equation $u_{tt} 
 + 2a(x) u_t = \\Delta_x u$ with an unbounded damping coefficient $a$\, e.g
 .~$a(x) = x^2$\, $x \\in \\mathbb R$. The key step is the study of the ass
 ociated quadratic operator function $T(\\lambda) = -\\Delta + 2 \\lambda a
 (x) + \\lambda^2$\, $\\lambda \\in \\mathbb C$. Due to the form of this fu
 nction\, some of the recently developed techniques of the spectral theory 
 for Schr\\"odinger operator with complex potential can be generalized\; in
  particular the pseudomode construction and upper resolvent norm estimates
 . Moreover\, the latter and recent results in semigroup theory provide an 
 estimate on the decay of solutions as $t \\to + \\infty$.\n\nThe talk is b
 ased mainly on joint works with A. Arnal.\n\nhttps://indico.math.cnrs.fr/e
 vent/10296/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/10296/
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