Upper semicontinuity of the global attractor for Bresse system with second sound

Pub Date : 2023-02-23 DOI:10.1080/14689367.2023.2182182
M. Freitas, A. Ramos, M. Aouadi, D. S. Almeida Júnior
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Abstract

In this paper, we study the long-time dynamics of Bresse system under mixed homogeneous Dirichlet–Neumann boundary conditions. The heat conduction is given by Cattaneo's law. Only the shear angle displacement is damped via the dissipation from the Cattaneo's law, and the vertical displacement and the longitudinal displacement are free. Under quite general assumptions on the source term and based on the semigroup theory, we establish the global well-posedness and the existence of global attractors with finite fractal dimension in natural space energy. Finally, we prove the upper semicontinuous with respect to the relaxation time τ as it converges to zero.
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具有第二声的Bresse系统全局吸引子的上半连续性
本文研究了混合齐次Dirichlet-Neumann边界条件下Bresse系统的长时间动力学问题。热传导由卡塔尼奥定律给出。只有剪切角位移通过卡塔内奥定律的耗散得到阻尼,垂直位移和纵向位移是自由的。在相当一般的源项假设下,基于半群理论,建立了自然空间能量中分形维数有限的全局吸引子的全局适定性和存在性。最后,我们证明了当松弛时间τ收敛于零时,上半部分是连续的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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