We consider the initial value problem for a nonlinear version of the dissipative Timoshenko system. This syetem verifies the decay property of regularity-loss type. To overcome this difficulty caused by the regularity-loss property, we employ the time weighed L2 energy method which is combined with the optimal L2 decay estimates for lower order derivatives of solutions. Then we show the global existence and asymptotic decay of solutions under smallness and enough regularity conditions on the initial data. Moreover, we show that the solution approaches the linear diffusion wave expressed in terms of the superposition of the heat kernels as time tends to infinity.
|ジャーナル||Mathematical Models and Methods in Applied Sciences|
|出版物ステータス||Published - 2008 7 1|
ASJC Scopus subject areas
- Modelling and Simulation
- Applied Mathematics