On the asymptotic properties of solutions to a nonlinear transmission problem for a Bresse beam with thermal damping

Fuente: arXiv
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Main Authors: Fastovska, Tamara, Langemann, Dirk
Format: Preprint
Published: 2025
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_version_ 1866909705308209152
author Fastovska, Tamara
Langemann, Dirk
author_facet Fastovska, Tamara
Langemann, Dirk
contents A nonlinear transmission problem for an arch beam, which consists of two parts with different material properties is considered. One of the parts is subjected to thermal damping while another one is undamped. The thermal damping affects only the shear angle and the longitudinal equation within the damped part, which can have any positive length. We prove the well-posedness of the system in the energy space and establish the existence of a compact global attractor under certain conditions imposed solely on the coefficients of the damped part. Additionally, we study singular limits of the system as the curvature of the beam tends to zero or in case both the curvature vanishes and the shear moduli tend to infinity. Numerical simulations are also carried out to model these limiting behaviors.
format Preprint
id arxiv_https___arxiv_org_abs_2507_19297
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the asymptotic properties of solutions to a nonlinear transmission problem for a Bresse beam with thermal damping
Fastovska, Tamara
Langemann, Dirk
Analysis of PDEs
35B41, 35B25 (Primary) 74K10 (Secondary)
A nonlinear transmission problem for an arch beam, which consists of two parts with different material properties is considered. One of the parts is subjected to thermal damping while another one is undamped. The thermal damping affects only the shear angle and the longitudinal equation within the damped part, which can have any positive length. We prove the well-posedness of the system in the energy space and establish the existence of a compact global attractor under certain conditions imposed solely on the coefficients of the damped part. Additionally, we study singular limits of the system as the curvature of the beam tends to zero or in case both the curvature vanishes and the shear moduli tend to infinity. Numerical simulations are also carried out to model these limiting behaviors.
title On the asymptotic properties of solutions to a nonlinear transmission problem for a Bresse beam with thermal damping
topic Analysis of PDEs
35B41, 35B25 (Primary) 74K10 (Secondary)
url https://arxiv.org/abs/2507.19297