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This work first gives the global existence and optimal decay rates ofsolutions to the classical Timoshenko system on the framework of Besov spaces.Due to the \textit{non-symmetric} dissipation, the general theory fordissipative hyperbolic systems ([30]) can not be applied to the Timoshenkosystem directly. In the case of equal wave speeds, we construct globalsolutions to the Cauchy problem pertaining to data in the spatially Besovspaces. Furthermore, the dissipative structure enables us to give a new decayframework which pays less attention on the traditional spectral analysis.Consequently, the optimal decay estimates of solution and its derivatives offractional order are shown by time-weighted energy approaches in terms oflow-frequency and high-frequency decompositions. As a by-product, the usualdecay estimate of $L^{1}(\mathbb{R})$-$L^{2}(\mathbb{R})$ type is also shown.

Global existence and optimal decay rates for the Timoshenko system: the case of equal wave speeds