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  • exponential decay  (3)
  • Springer  (3)
  • Oxford University Press
  • 1
    Electronic Resource
    Electronic Resource
    Decay rates for viscoelastic plates with memory (1996)
    Springer
    Journal of elasticity 44 (1996), S. 61-87 
    Details
    ISSN: 1573-2681
    Keywords: 35B40 ; 35L05 ; 35L70 ; viscoelasticity ; exponential decay ; initial boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract We consider the viscoelastic plate equation and we prove that the first and second order energies associated with its solution decay exponentially provided the kernel of the convolution also decays exponentially. When the kernel decays polynomially then the energy also decays polynomially. More precisely if the kernel g satisfies g(t) ⩽ -c0g(t)1+1/p and g,g1+1/p ∈ L1(ℝ) with p 〉 2, then the energy decays as 1/(1+t)p.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00042192
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  • 2
    Electronic Resource
    Electronic Resource
    The Transmission Problem of Viscoelastic Waves (2000)
    Springer
    Acta applicandae mathematicae 62 (2000), S. 1-21 
    Details
    ISSN: 1572-9036
    Keywords: transmission problem ; exponential decay ; partially viscoelastic ; materials with memory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider the transmission problem of viscoelastic waves. That is, we study the wave propagations over materials consisting of elastic and viscoelastic components. We show that for this types of materials the dissipation produced by the viscoelastic part is strong enough to produce exponential decay of the solution, no matter how small is its size. We also show that the linear model is well posed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006449032100
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  • 3
    Electronic Resource
    Electronic Resource
    Uniform Rates of Decay in Anisotropic Thermo-Viscoelasticity (1998)
    Springer
    Acta applicandae mathematicae 50 (1998), S. 207-224 
    Details
    ISSN: 1572-9036
    Keywords: viscoelasticity ; exponential decay ; initial boundary-value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the anisotropic and inhomogeneous thermo-viscoelastic equation. We prove that the first and second-order energy decay exponentially as time goes to infinity provided the relaxation function also decays exponentially to zero. While if the relaxation functions decay polynomially to zero, then the energy decays also polynomially. That is, the kernel of the convolution defines the rate of decay of the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005830811242
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