Spectral perturbations in linear viscoelasticity of the Boltzmann type

J. Cainzos; M. Lobo-Hidalgo

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1985)

  • Volume: 19, Issue: 4, page 559-572
  • ISSN: 0764-583X

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Cainzos, J., and Lobo-Hidalgo, M.. "Spectral perturbations in linear viscoelasticity of the Boltzmann type." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 19.4 (1985): 559-572. <http://eudml.org/doc/193459>.

@article{Cainzos1985,
author = {Cainzos, J., Lobo-Hidalgo, M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {spectral perturbations; algebroid singularity; vibration frequencies; linear viscoelastic materials of Boltzmann type; second order systems; elliptic operators; existence of analytic branches; abstract evolution equation; reduction to a finite dimensional problem; Weierstrass preparation theorem},
language = {eng},
number = {4},
pages = {559-572},
publisher = {Dunod},
title = {Spectral perturbations in linear viscoelasticity of the Boltzmann type},
url = {http://eudml.org/doc/193459},
volume = {19},
year = {1985},
}

TY - JOUR
AU - Cainzos, J.
AU - Lobo-Hidalgo, M.
TI - Spectral perturbations in linear viscoelasticity of the Boltzmann type
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1985
PB - Dunod
VL - 19
IS - 4
SP - 559
EP - 572
LA - eng
KW - spectral perturbations; algebroid singularity; vibration frequencies; linear viscoelastic materials of Boltzmann type; second order systems; elliptic operators; existence of analytic branches; abstract evolution equation; reduction to a finite dimensional problem; Weierstrass preparation theorem
UR - http://eudml.org/doc/193459
ER -

References

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  1. [1] S. BOCHNER and W. T. MARTIN, Several Complex Variables, Princeton, Univ.Press, Princeton (1948). Zbl0041.05205MR27863
  2. [2] C. M. DAFERMOS, An abstract Volterra equation with application to linear viscoelasticity, J. Diff. Equations, 7 (1970), pp. 554-569. Zbl0212.45302MR259670
  3. [3] C. M. DAFERMOS, Asymptotic stability in viscoelasticity, Arch. Rat. Mech. Anal., 37 (1970), pp. 297-308. Zbl0214.24503MR281400
  4. [4] C. M. DAFERMOS, Contraction semigroups and trend to equilibrium in continuum mechanics, Lect. Notes Math., 503, Springer, Berlin (1975), pp. 295-306. Zbl0345.47032
  5. [5] T. KATO, Perturbation Theory for Linear Operators, Springer, Berlin (1966). Zbl0148.12601
  6. [6] K. KNOPP, Theory of Function, II, Dover, New York (1947). MR19722
  7. [7] M. LOBO-HIDALGO, Propriétés spectrales de certaines équations différentielles intervenant en viscoélasticité, Rend. Sem. Mat. Univ. Polit. Torino, 39 (1981), Zbl0489.73063MR660992
  8. [8] Ph. NOVERRAZ, Fonctions plurisousharmoniques et analytiques dans les espaces vectoriels topologiques complexes, Ann. Inst. Fourier, t. XIX, fasc. 2 (1970),pp. 419-493. Zbl0176.09903MR265628
  9. [9] R. OHAYON and E. SANCHEZ-PALENCIA, On the vibration problem for an elastic body surrounded by a slïghtly compressible fluid, R.A.I.R.O. Analyse Numérique,17, n° 3 (1983), pp. 311-326. Zbl0513.73055MR702140
  10. [10] E. SANCHEZ-PALENCIAFréquences de diffusion dans le problème de vibration d'un corps élastique plongé dans un fluide compressible de petite densité, C. R. Acad. Se. Paris, t. 295 (1982), pp. 197-200. Zbl0501.76062MR676397
  11. [11] N. TURBE, On two scales method for a class of integrodifferential equations appearing in viscoelasticity, Int. Jour. Engin. Sci. (1979), pp. 857-868. Zbl0412.73002MR659194

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