TY - JOUR
T1 - Decay property for the timoshenko system with fourier's type heat conduction
AU - Mori, Naofumi
AU - Kawashima, Shuichi
AU - LeFloch, P. G.
N1 - Funding Information:
The first author (N.M.) would like to express his heartiest thanks to Professor Tohru Nakamura at Kyushu University, Professor Yoshihiro Ueda at Kobe University, and Professor Hiroshi Takeda at Fukuoka Institute of Technology for giving him valuable advices and helpful comments. This work was supported in part by Grant-in-Aid for Scientific Research (A) 22244009.
PY - 2014/3
Y1 - 2014/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84896949962&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84896949962&partnerID=8YFLogxK
U2 - 10.1142/S0219891614500039
DO - 10.1142/S0219891614500039
M3 - Article
AN - SCOPUS:84896949962
SN - 0219-8916
VL - 11
SP - 135
EP - 157
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
IS - 1
ER -