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Initial value problems in elasticity. (English) Zbl 0790.35108
Bojarski, Bogdan (ed.) et al., Partial differential equations. Part 1. The 36th semester held at the Stefan Banach International Mathematical Center in Warsaw, Poland, from September 17 to December 17, 1990. Warsaw: Polish Academy of Sciences, Inst. of Mathematics. Banach Cent. Publ. 27, Part 1, 277-294 (1992).
The author presents the results concerning the initial-boundary value problem for the wave equation in homogeneous and anisotropic elastic media. After giving a survey of state-of the art of the problem for linear and nonlinear wave equations, he reports some new results describing wave propagation in elastic medium with cubic symmetry. Taking for simplicity a medium in \(\mathbb{R}^ 2\), the author proves the existence of global smooth solutions of the quasi-linear system of elasticity with initial cubic symmetry under a restriction on the nonlinear terms.
For the entire collection see [Zbl 0771.00021].
Reviewer: O.Titow (Berlin)

35Q72 Other PDE from mechanics (MSC2000)
74B20 Nonlinear elasticity
35L15 Initial value problems for second-order hyperbolic equations