Asymptotic behaviour of solutions to transmission problems for full von Karman elastic beamsOberseminar Analysis

by Dr Tamara Fastovska (Humboldt Univ. zu Berlin)

Thursday Jun 25, 2026, 2:15 PM → 4:15 PM Europe/Berlin

Endenicher Allee 60/2. OG.-040 - Room 2.040 (Mathezentrum)

We will 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 structural damping acting only on one part of the domain. Such transmission systems 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 dissipativity are not sufficient. Instead, we prove asymptotic smoothness of the associated dynamical system and investigate its gradient structure. A key ingredient of the analysis is the proof of a unique continuation property for stationary solutions. This property is obtained through suitable Carleman estimates adapted to the transmission geometry and allows us to show that the energy dissipation mechanism acting on only a portion of the beam is sufficient to determine the behavior of the entire structure. As a consequence, a strict Lyapunov functional is constructed, yielding the gradient property of the dynamical system.