Exponential stability for the Timoshenko system with two weak dampings. (English) Zbl 1072.74033

Raposo, Carlos Alberto; Ferreira, Jorge; Santos, Mauro Lima; Castro, N. N. O.

Appl. Math. Lett. 18, No. 5, 535-541 (2005).

Summary: We consider a linear system of Timoshenko type beam equations with frictional dissipative terms. We show the exponential decay of the solution by using a method developed by Z. Liu and S. Zheng [Semigroups associated with dissipative systems. Chapman & Hall/CRC Research Notes in Mathematics. 398. Boca Raton, FL: Chapman & Hall/CRC (1999; Zbl 0924.73003)] and their collaborators in past years. This method is very different from some others in the literature, such as the traditional energy method. It is our hope that the reader will find that the method presented in this work is powerful and simple.

MSC:

74H45	Vibrations in dynamical problems in solid mechanics
74H40	Long-time behavior of solutions for dynamical problems in solid mechanics
74K10	Rods (beams, columns, shafts, arches, rings, etc.)
47N60	Applications of operator theory in chemistry and life sciences

Keywords:

Lyapunov functional; semigroup of contractions; Hilbert space

Citations:

Zbl 0924.73003

References:

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