DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION

作者：Liu, Yongqin; Kawashima, Shuichi^*

来源：Mathematical Models and Methods in Applied Sciences, 2012, 22(2): 1150012.

DOI：10.1142/S0218202511500126

• Timoshenko system with memory
• pointwise estimate in the Fourier space
• decay property
• regularity-loss type

In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier-Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

• 出版日期2012-2
• 单位华北电力大学