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Decay Estimates for Solutions of Linear Elasticity for Anisotropic Media
Author(s) -
Stoth Markus
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960110)19:1<15::aid-mma758>3.0.co;2-g
Subject(s) - mathematics , degenerate energy levels , elasticity (physics) , anisotropy , isotropy , mathematical analysis , cauchy distribution , linear elasticity , physics , quantum mechanics , thermodynamics , finite element method
We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to ℒ p –ℒ q ‐estimates.