Decay property of regularity-loss type for dissipative timoshenko system

We study the decay property of the dissipative Timoshenko system in the one-dimensional whole space. We derive the L² decay estimates of solutions in a general situation and observe that this decay structure is of the regularity-loss type. Also, we give a refinement of these decay estimates for some special initial data. Moreover, under enough regularity assumption on the initial data, we show that the solution approaches the linear diffusion wave expressed in terms of the heat kernels as time tends to infinity. The proof is based on the detailed pointwise estimates of solutions in the Fourier space.