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SUMMARY:Asymptotic behaviour of solutions to transmission problems for ful
 l von Karman elastic beams [Oberseminar Analysis]
DTSTART:20260625T121500Z
DTEND:20260625T141500Z
DTSTAMP:20260716T202800Z
UID:indico-event-1389@math-events.uni-bonn.de
DESCRIPTION:Speakers: Tamara Fastovska (Humboldt Univ. zu Berlin)\n\nWe wi
 ll discuss the long-time behavior of solutions to a nonlinear transmission
  problem for an elastic beam governed by the full von Kármán model. The 
 beam consists of two coupled segments separated by an interface\, with str
 uctural damping acting only on one part of the domain. Such transmission s
 ystems arise naturally in the modeling of composite elastic structures and
  heterogeneous materials. The main objective is to describe the asymptotic
  dynamics of solutions. Owing to the highly nonlinear coupling produced by
  the full von Kármán terms\, standard methods based on direct dissipativ
 ity are not sufficient. Instead\, we prove asymptotic smoothness of the as
 sociated dynamical system and investigate its gradient structure. A key in
 gredient of the analysis is the proof of a unique continuation property fo
 r stationary solutions. This property is obtained through suitable Carlema
 n estimates adapted to the transmission geometry and allows us to show tha
 t the energy dissipation mechanism acting on only a portion of the beam is
  sufficient to determine the behavior of the entire structure. As a conseq
 uence\, a strict Lyapunov functional is constructed\, yielding the gradien
 t property of the dynamical system.\n \n\nhttps://math-events.uni-bonn.de
 /event/1389/
LOCATION:Endenicher Allee 60/2. OG.-040 - Room 2.040 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1389/
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