Advances in Differential Equations

Classical solutions of the Timoshenko system

R. Grimmer and E. Sinestrari

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Abstract

We prove the existence and uniqueness of a $C^2$--solution of the Timoshenko system for the motion of an elastic beam. In addition, we give pointwise estimates for the displacement, rotation, shear angle and their derivatives with constants explicitly calculated. The method of proof is based on the Hille--Yosida operator theory.

Article information

Source
Adv. Differential Equations, Volume 7, Number 7 (2002), 799-818.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651706

Mathematical Reviews number (MathSciNet)
MR1895166

Zentralblatt MATH identifier
1030.74021

Subjects
Primary: 74H20: Existence of solutions
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 35Q72 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 74H25: Uniqueness of solutions 74K10: Rods (beams, columns, shafts, arches, rings, etc.)

Citation

Grimmer, R.; Sinestrari, E. Classical solutions of the Timoshenko system. Adv. Differential Equations 7 (2002), no. 7, 799--818. https://projecteuclid.org/euclid.ade/1356651706


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