TY - JOUR
T1 - Decay property for the timoshenko system with memory-type dissipation
AU - Liu, Yongqin
AU - Kawashima, Shuichi
N1 - Funding Information:
This work was partially supported by the Fundamental Research Funds for the Central Universities (11ML31) and also by Grant-in-Aid for JSPS Fellows. The second author is partially supported by Grant-in-Aid for Scientific Research (A) No. 22244009.
PY - 2012/2
Y1 - 2012/2
N2 - 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.
AB - 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.
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U2 - 10.1142/S0218202511500126
DO - 10.1142/S0218202511500126
M3 - Article
AN - SCOPUS:84856615722
SN - 0218-2025
VL - 22
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 2
M1 - 1150012-1
ER -