Decay rates and global existence for semilinear dissipative Timoshenko systems
The main goal of this paper is to prove optimal decay estimates for the dissipative Timoshenko system in the one-dimensional whole space, and to prove a global existence theorem for semilinear systems. More precisely, if we restrict the initial data ((φ0,ψ0),(φ1,ψ1)) ∈ ( Hs+1 ( RN ) ∩L1,γ ( RN )) × ( Hs ( RN ) ∩L1,γ ( RN )) with γ ∈ [0,1], then we can derive faster decay estimates than those given in [8]. Then, we use these decay estimates of the linear problem combined with the weighted energy method introduced by Todorova and Yordanov [35] with the special weight given in [11], to tackle a semilinear problem.