Well-posedness and energy decay for Timoshenko systems with discrete time delay under frictional damping and/or infinite memory in the displacement View Full Text


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Article Info

DATE

2017-12

AUTHORS

Aissa Guesmia

ABSTRACT

In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain with discrete time delay and complementary frictional damping and infinite memory controls all acting on the transversal displacement. We show that the system is well-posed in the sens of semigroup and that, under appropriate assumptions on the weights of the delay and the history data, the stability of the system holds in case of the equal-speed propagation as well as in the opposite case in spite of the presence of a discrete time delay, where the decay rate of solutions is given in terms of the smoothness of the initial data and the growth of the relaxation kernel at infinity. The results of this paper extend the ones obtained by the present author and Messaoudi in (Acta Math Sci 36:1–33, 2016) to the case of presence of discrete delay. More... »

PAGES

1253-1284

References to SciGraph publications

  • 2002-05. Indirect internal stabilization of weakly coupled evolution equations in JOURNAL OF EVOLUTION EQUATIONS
  • 2014-12. Stability to 1-D thermoelastic Timoshenko beam acting on shear force in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 2008-12. On the Internal and Boundary Stabilization of Timoshenko Beams in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
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  • 1970-01. Asymptotic stability in viscoelasticity in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2005-01. Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems in APPLIED MATHEMATICS & OPTIMIZATION
  • 2010-04. General energy decay rates for a weakly damped Timoshenko system in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2007-12. Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 1983. Semigroups of Linear Operators and Applications to Partial Differential Equations in NONE
  • 2009-10. On the Stability of Damped Timoshenko Systems: Cattaneo Versus Fourier Law in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • Journal

    TITLE

    Afrika Matematika

    ISSUE

    7-8

    VOLUME

    28

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s13370-017-0514-8

    DOI

    http://dx.doi.org/10.1007/s13370-017-0514-8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1090322070


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