Advances in Differential Equations

Classical solutions of the Timoshenko system

R. Grimmer and E. Sinestrari

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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

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

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.)


Grimmer, R.; Sinestrari, E. Classical solutions of the Timoshenko system. Adv. Differential Equations 7 (2002), no. 7, 799--818.

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