New Stability Results for a Linear Thermoelastic Bresse System with Second Sound View Full Text


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Article Info

DATE

2019-02-26

AUTHORS

M. Afilal, A. Guesmia, A. Soufyane

ABSTRACT

In this paper, we consider a linear one-dimensional thermoelastic Bresse system with second sound consisting of three hyperbolic equations and two parabolic equations coupled in a certain manner under mixed homogeneous Dirichlet–Neumann boundary conditions, where the heat conduction is given by Cattaneo’s law. Only the longitudinal displacement is damped via the dissipation from the two parabolic equations, and the vertical displacement and shear angle displacement are free. We prove the well-posedness of the system and some exponential, non exponential and polynomial stability results depending on the coefficients of the equations and the smoothness of initial data. Our method of proof is based on the semigroup theory and a combination of the energy method and the frequency domain approach. More... »

PAGES

699-738

References to SciGraph publications

  • 1994. Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures in NONE
  • 2016-12-29. Third Hankel Determinants for Subclasses of Univalent Functions in MEDITERRANEAN JOURNAL OF MATHEMATICS
  • 2014-01-02. The twisted Daehee numbers and polynomials in ADVANCES IN DIFFERENCE EQUATIONS
  • 2005-07. Characterization of polynomial decay rate for the solution of linear evolution equation in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 1983. Semigroups of Linear Operators and Applications to Partial Differential Equations in NONE
  • 2016-09-01. Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound in APPLIED MATHEMATICS & OPTIMIZATION
  • 2008-05-30. Energy decay rate of the thermoelastic Bresse system in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 2016-09-19. Uniform and weak stability of Bresse system with two infinite memories in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
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    http://scigraph.springernature.com/pub.10.1007/s00245-019-09560-7

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    http://dx.doi.org/10.1007/s00245-019-09560-7

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