论文信息 - Exponential decay of Timoshenko systems with indefinite memory dissipation

Exponential decay of Timoshenko systems with indefinite memory dissipation

We study the asymptotic behavior of Timoshenko systems with memory, where the memory is given by a non-dissipative kernel and is acting only on one equation of the system. We show that the exponential stability depends on conditions regarding the decay rate of the kernel and a nice relationship between the coefficients of the system. Moreover, with full-memory effect in the system, we will show exponential stability in the general case.

Jaime E. Muñoz Rivera | Hugo D. Fernández Sare | J. M. Rivera | H. F. Sare

[1] Jaime E. Muñoz Rivera,et al. On the decay of the energy for systems with memory and indefinite dissipation , 2006, Asymptot. Anal..

[2] Michael Renardy,et al. On the Type of Certain Co-Semigroups , 1993 .

[3] Larry Gearhart,et al. Spectral theory for contraction semigroups on Hilbert space , 1978 .

[4] H. F. Sare,et al. Stability of Timoshenko systems with past history , 2008 .

[5] R. Racke,et al. Mildly dissipative nonlinear Timoshenko systems—global existence and exponential stability☆ , 2002 .

[6] R. Racke,et al. Energy decay for Timoshenko systems of memory type , 2003 .

[7] Jaime E. Muñoz Rivera,et al. Global stability for damped Timoshenko systems , 2003 .

[8] J. Prüss. On the Spectrum of C 0 -Semigroups , 1984 .

[9] Zhuangyi Liu,et al. Semigroups Associated with Dissipative Systems , 1999 .

[10] Abdelaziz Soufyane,et al. Stabilisation de la poutre de Timoshenko , 1999 .