The evolution laws of dilatational spherical and cylindrical weak nonlinear shock waves in elastic non-conductors. (English) Zbl 0691.73017
In the paper the evolution equations of dilatational spherical and cylindrical weakly nonlinear shock waves in elastic non-conductors is discussed. This includes some coupled equations giving the shock amplitude and the higher order discontinuities accompanying the shock process. The taken approach involves the use of the perturbation method with a perturbation parameter \(\epsilon\). The obtained results are compared to those known in nonlinear optics and this leads to a good agreement. We think the paper represents a fundamental contribution in the area of shock waves.
Reviewer: D.Stanomir
MSC:
| 74J10 | Bulk waves in solid mechanics |
| 74B20 | Nonlinear elasticity |
| 35B20 | Perturbations in context of PDEs |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 78A05 | Geometric optics |
| 74M20 | Impact in solid mechanics |
| 74J99 | Waves in solid mechanics |
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