Geodesic
Reduction of the Cosserat-type nonlinear equations to the system of Godunov's form
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 55-64

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The complete system of equations for the dynamics of a Cosserat-type continuum with finite strains and particle rotations in Lagrangian variables is reduced to a compatible system of conservation laws in the Godunov sense. This system allows one to analyse generalized solutions with surfaces of strong discontinuity of stresses and velocities and admits integral estimates. They guarantee the uniqueness and continuity of solutions of the Cauchy problem and boundary-value problems with dissipative boundary conditions in relation to initial data.
Keywords: elasticity, Cosserat continuum, couple stress tensor, curvature tensor. 
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     title = {Reduction of the {Cosserat-type} nonlinear equations to the system of  {Godunov's} form},
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Vladimir M. Sadovskii. Reduction of the Cosserat-type nonlinear equations to the system of  Godunov's form. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 55-64. http://geodesic.mathdoc.fr/item/JSFU_2024_17_1_a6/