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Nonlinear waves in elastic media. (English) Zbl 0865.73004
Boca Raton, FL: CRC Press. 237 p. (1995).
The authors survey theoretical results obtained over the last 15 years on one-dimensional nonlinear waves, first of all on shock waves in elastic media. Emphasis is placed on quasi-transverse waves, and an essential part of the volume concerns small amplitude nonlinear waves in elastic media; this study can be considered as exhaustive. Additionally, the authors present general mathematical methods suitable for treating nonlinear hyperbolic conservation laws.
The book, is divided into nine chapters; 1. Mathematical introduction; 2. On plane wave problems in elastic media; 3. Riemann waves; 4. Shock waves; 5. Unsteady self-similar problems for small amplitude waves; 6. Two-dimensional steady nonlinear waves and self-similar solutions; 7. Simplified equations. Nonself-similar problems; 8. Viscous-elastic medium motion; 9. Finite amplitude waves in weakly anisotropic media. An index and a large list of references (66 titles) complete this book which can be considered as a very important contribution to the field.

MSC:
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74J10 Bulk waves in solid mechanics
74M20 Impact in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
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