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Zbl 1043.35009
Burq, Nicolas; Lebeau, Gilles
Microlocal defect measures, application to the Lamé system. (Mesures de défaut de compacité, application au système de Lamé.) (French)
[J] Ann. Sci. Éc. Norm. Supér. (4) 34, No. 6, 817-870 (2001). ISSN 0012-9593

Many authors, including the second author of this paper, have studied the asymptotic propagation of the energy for the solutions of systems of PDEs. In this paper generalizations of some well-known results are obtained. The key is the proposed definition of the microlocal defect measures for boundary value systems satisfying the strong Lopatinski condition. The proof of the theorem of propagation given is interesting. The imposed condition implies naturally the limit condition of Lopatinski type. Applications for the solutions of the Lame system are obtained. A description of the theorem of propagation for the transversal wave when the longitudinal energy is negligible. Finally, the conjecture of {\it G. Lebeau} and {\it E. Zuazua} [Arch. Ration. Mech. Anal. 148, No. 3, 179--231 (1999; Zbl 0939.74016)] is proved.
[Stanco Dimiev (Sofia)]

MSC 2000:: *35A27 Sheaf-theoretic methods (PDE)
35A21 Propagation of singularities
74B20 Nonlinear elasticity
35Q72 Other PDE from mechanics
35L20 Second order hyperbolic equations, boundary value problems
58J15 Relations with hyperfunctions
74F05 Thermal effects
74G99 Equilibrium (steady-state) problems

Keywords: Lopatinski condition; asymptotic propagation

Citations: Zbl 0939.74016

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