Repubshenko系统的全局存在性和最优衰减率：等波速的情况
Global existence and optimal decay rates for the Timoshenko system: the case of equal wave speeds
摘要：
本文首先在Besov空间的框架下给出了经典Beshenko系统解的整体存在性和最优衰减率。由于\textit{non-symmetric}的耗散性，耗散双曲型方程组的一般理论（[30]）不能直接应用于Eschlishenko方程组。在相同的波速的情况下，我们构造整体解决方案的柯西问题的数据在空间Besov空间。此外，耗散结构使我们能够给出一个新的衰变框架，而不是传统的谱分析。利用时间加权能量方法，给出了解及其分数阶导数在低频和高频分解下的最优衰减估计。作为副产品，还显示了$L^{1}(\mathbb{R})$ - $L^{2}(\mathbb{R})$型的通常衰变估计。
英文摘要：
This work first gives the global existence and optimal decay rates of solutions to the classical Timoshenko system on the framework of Besov spaces. Due to the \textit{non-symmetric} dissipation, the general theory for dissipative hyperbolic systems ([30]) can not be applied to the Timoshenko system directly. In the case of equal wave speeds, we construct global solutions to the Cauchy problem pertaining to data in the spatially Besov spaces. Furthermore, the dissipative structure enables us to give a new decay framework which pays less attention on the traditional spectral analysis. Consequently, the optimal decay estimates of solution and its derivatives of fractional order are shown by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As a by-product, the usual decay estimate of $L^{1}(\mathbb{R})$-$L^{2}(\mathbb{R})$ type is also shown.
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