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This chapter 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 the 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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Attractors for Locally Damped Bresse Systems and a Unique Continuation Property

  • 章节

  • 发表日期：

    2025年

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  • To Fu Ma,
  • Rodrigo N. Monteiro,
  • Paulo N. Seminario-Huertas

摘要

This chapter 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 the 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.