发表机构
Institute for Advanced Study, Shenzhen University; Department of Mathematics, Faculty of Science, Kunming University of Science and Technology（深圳大学高等研究院; 昆明理工大学理学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过局部压力反馈镇定深水中二维周期水弹性波，证明均匀时空估计与耗散可观测性，实现哈密顿量定量衰减，方法结合能量耗散与非线性乘子法。
AI 中文摘要
我们考虑在无质量非线性Cosserat薄板下方的深水中，通过局部压力反馈对二维周期水弹性波进行镇定。对于足够正则的解，在涉及重力、弯曲刚度和局部化剖面的显式条件下，我们证明了均匀时空估计和局部耗散可观测性不等式。因此，只要解保持在小几何范围内，水弹性哈密顿量就会定量衰减。证明结合了能量耗散恒等式与适用于无限深度几何的非线性乘子方法，以及对Cosserat弯曲能量的强制性分析。
英文摘要
We consider the stabilization of two-dimensional periodic hydroelastic waves in deep water beneath a massless nonlinear Cosserat sheet by means of a localized pres- sure feedback. For sufficiently regular solutions, under an explicit condition relating gravity, flexural rigidity and the localization profile, we prove a uniform spacetime estimate and a localized dissipation observability inequality. As a consequence, the hydroelastic Hamiltonian decays quantitatively as long as the solution remains in a small geometric regime. The proof combines an energy dissipation identity with a nonlinear multiplier method adapted to the infinite-depth geometry, together with a coercivity analysis of the Cosserat bending energy.
