Attractors for locally damped Bresse systems and a unique continuation property

2021/02/24 by To Fu, Ma, To Fu, Rodrigo Nunes Monteiro +3
Computer Science · Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2102.12025

openalex publication_date 2021/02/24 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to Bresse systems, a robust model for circular beams, given by a set of three coupled wave equations. The main objective is to establish the existence of global attractors for dynamics of semilinear problems with localized damping. In order to deal with localized damping a unique continuation property (UCP) is needed. Therefore we also provide a suitable UCP for Bresse systems. Our strategy is to set the problem in a Riemannian geometry framework and see the system as a single equation with different Riemann metrics. Then we perform Carleman-type estimates to get our result.

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