Behaviour of the energy density associated to a Kelvin-Voight model in viscoelasticity

Asymptotic Analysis

Volumn 34, Issue 3-4, 2003, Pages 261-273

  Petrini, Milena ^a  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; FUNCTIONS; INITIAL VALUE PROBLEMS; MATHEMATICAL MODELS;

ENERGY DENSITY; EXPONENTIAL DECAY; KELVIN-VOIGHT MODEL;

VISCOELASTICITY;

EID: 0037767906     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. A. Bensoussan, J.-L. Lions and G. Papanicolau, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
2. G.A. Chechkin, Operator pencil and homogenization in the problem of vibration of fluid in a vessel with a fine net on the surface, IMA Preprint Series # 1367, 1995.
3. C. Conca and M. Vanninathan, Homogenization of periodic structure via Bloch decomposition, SIAM J. Appl. Math. 57(6) (1997), 1639-1659.
4. G.A. Francfort and F. Murat, Oscillations and energy densities in the wave equation, Comm. Partial Differential Equations 17(11 & 12) (1992), 1785-1865.
5. P. Gerard, Mesures semi-classiques et ondes de Bloch, in: Séminaire sur les Équations aux Dérivées Partielles, 1990-1991, Exp. No. XVI, École polytechnique, Palaiseau, 1991.
6. P. Gerard, P. Markowich, N. Mauser and F. Poupaud, Homogenization limits and Wigner transforms, Comm. Pure Appl. Math. L (1997), 323-379.
7. P.-L. Lions and T. Paul, Sur les mesures de Wigner, Rev. Mat. Iberoamericana 9 (1993), 553-618.
8. T. Kato, Perturbation Theory for Linear Operators, 2nd edn, Springer, 1980.
9. A. S. Markus, Introduction to the Spectral Theory of Polynomial Operator Pencils, Translations of Mathematical Monographs, 1988.
10. O.A. Oleinik, A.S. Shamaev and G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, 1992.
11. M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators, Academic Press, 1987.
12. L. Tartar, H-measures, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Rov. Soc. Edinburgh Sect. A 115 (1990), 193-230.
13. C.H. Wilcox, Theory of Bloch waves, J. Anal. Math. 33 (1978), 146-167.