Stability of Mindlin-Timoshenko plate with nonlinear boundary damping and boundary sources

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• 作者：Pei Pei ^{ppei@otterbein.edu}
• 关键词：Mindlin&ndash ; Timoshenko plate ; Boundary damping ; Boundary sources ; Potential well ; Stability ; Decay rates
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1467-1488
• 全文大小：479 K
• 卷排序：448

文摘

Presented here is a study of long-term behavior of Mindlin–Timoshenko (RMT) plate systems, focusing on the interplay between nonlinear viscous boundary damping and boundary source terms. This work complements [28] which established local well-posedness of this problem, and global well-posedness when the boundary damping dominates the boundary sources (in an appropriate sense). The current paper develops the potential well theory for the RMT system: global existence for potential well solutions without restricting the boundary source exponents, and explicit energy decay rates dependent on the boundary damping exponents. This work along with ,  and  provides the fundamental well-posedness and stability theory for MT plates under the interplay of damping and source terms acting either in the interior or on the boundary of the plate.