Geodesic
The evolutionary equation for one-dimensional shear waves of a~rupture of strains
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2011), pp. 91-104

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The problem about formation and the subsequent distribution of the one-dimensional shear shock wave in nonlinear elastic incompressible isotropic half-space is solved. Application of a method of the spliced asymptotic expansions in front field of a shock wave leads to the evolutionary quasilinear wave equation which is distinct from the equations of Hopf, characteristic for volume shock waves. Some methods of build-up of solutions for the evolutionary equations of the shift waves, allowing to consider the manifold time functions in the capacity of boundary conditions for a field of transitions, are offered.
Keywords: nonlinear elasticity, incompressibility, shock wave, evolutionary equation.
Mots-clés : method of perturbations 
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     author = {Yu. E. Ivanova and V. E. Ragozina},
     title = {The evolutionary equation for one-dimensional shear waves of a~rupture of strains},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {91--104},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2011_2_a9/}
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Yu. E. Ivanova; V. E. Ragozina. The evolutionary equation for one-dimensional shear waves of a~rupture of strains. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2011), pp. 91-104. http://geodesic.mathdoc.fr/item/VSGU_2011_2_a9/