Geodesic
Transport solutions of the Lamé equations and shock elastic waves
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1351-1362 
L. A. Alexeyeva; G. K. Kaishibaeva. Transport solutions of the Lamé equations and shock elastic waves. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1351-1362. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a12/
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     title = {Transport solutions of the {Lam\'e} equations and shock elastic waves},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented.

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