We study the Timoshenko system with Fourier's type heat conduction in the one-dimensional (whole) space. We observe that the dissipative structure of the system is of the regularity-loss type, which is somewhat different from that of the dissipative Timoshenko system studied earlier by Ide-Haramoto-Kawashima. Moreover, we establish optimal L2 decay estimates for general solutions. The proof is based on detailed pointwise estimates of solutions in the Fourier space. Also, we introuce here a refinement of the energy method employed by Ide-Haramoto-Kawashima for the dissipative Timoshenko system, which leads us to an improvement on their energy method.
ASJC Scopus subject areas
- 数学 (全般)