DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH FOURIER'S TYPE HEAT CONDUCTION

被引：34

作者：

Mori, Naofumi ^{[1
]}

Kawashima, Shuichi ^{[2
]}

机构：

[1] Kyushu Univ, Grad Sch Math, Fukuoka 8190395, Japan

[2] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2014年 / 11卷 / 01期

关键词：

Timoshenko system with thermal effects; decay property; asymptotic behavior; REGULARITY-LOSS TYPE; TRANSVERSE VIBRATIONS; TRANSMISSION PROBLEM; STABILITY; STABILIZATION;

D O I：

10.1142/S0219891614500039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 L-2 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.

引用

页码：135 / 157

页数：23

共 22 条

[1] Uniform stabilization for the transmission problem of the Timoshenko system with memory [J].

Alves, Margareth S. ;

Raposo, Carlos Alberto ;

Munoz Rivera, Jaime E. ;

Sepulveda, Mauricio ;

Vera Villagran, Octavio .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (01) :323-345

[2] Energy decay for Timoshenko systems of memory type [J].

Ammar-Khodja, F ;

Benabdallah, A ;

Rivera, JEM ;

Racke, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 194 (01) :82-115

[3] DISSIPATIVE PROPERTY OF THE VLASOV-MAXWELL-BOLTZMANN SYSTEM WITH A UNIFORM IONIC BACKGROUND [J].

Duan, Renjun .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2011, 43 (06) :2732-2757

[4] GLOBAL SMOOTH FLOWS FOR THE COMPRESSIBLE EULER-MAXWELL SYSTEM. THE RELAXATION CASE [J].

Duan, Renjun .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2011, 8 (02) :375-413

[5] Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system [J].

Hosono, Takafumi ;

Kawashima, Shuichi .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2006, 16 (11) :1839-1859

[6] Decay property of regularity-loss type for dissipative Timoshenko system [J].

Ide, Kentaro ;

Haramoto, Kazuo ;

Kawashima, Shuichi .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (05) :647-667

[7] DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION [J].

Liu, Yongqin ;

Kawashima, Shuichi .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2012, 22 (02)

[8]

Liu Z., 1998, Adv. Math. Sci. Appl, V8, P343

[9]

Raposo CA, 2007, COMPUT APPL MATH, V26, P215, DOI 10.1590/S1807-03022007000200003

[10] Exponential stability for the Timoshenko system with two weak dampings [J].

Raposo, CA ;

Ferreira, J ;

Santos, ML ;

Castro, NNO .

APPLIED MATHEMATICS LETTERS, 2005, 18 (05) :535-541

← 1 2 3 →