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Structures of longitudinal-torsional shock waves and special discontinuities in nonlinearly viscoelastic media with dispersion

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Abstract

Weakly nonlinear longitudinal-torsional waves in rods are considered. The structure of discontinuities in the solutions of the hyperbolic system of equations describing these waves is studied. Previously, the authors studied discontinuity structures under more special assumptions about dissipative processes in these structures. In the present study, no constraints are imposed on the matrix of dissipative coefficients except for positive definiteness. Conditions are formulated for the existence of special discontinuities, that is, discontinuities with additional boundary conditions that are independent of conservation laws.

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Acknowledgements

This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-265).

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    A. P. Chugainova & A. G. Kulikovskii

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  1. A. P. Chugainova
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  2. A. G. Kulikovskii
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Correspondence to A. P. Chugainova.

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Communicated by Andreas Öchsner.

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Chugainova, A.P., Kulikovskii, A.G. Structures of longitudinal-torsional shock waves and special discontinuities in nonlinearly viscoelastic media with dispersion. Continuum Mech. Thermodyn. 35, 1655–1669 (2023). https://doi.org/10.1007/s00161-022-01182-9

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