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Young measures and an application of compensated compactness to one- dimensional nonlinear elastodynamics. (English) Zbl 0761.35061

In this interesting paper the author studies the Cauchy problem for a strictly hyperbolic nonlinear system of one dimensional nonlinear elasticity in Lagrangian coordinates. The existence of a convergent sequence of bounded approximating solutions is obtained by artificial viscosity and compensated compactness. With the same ingredients the author also proves the convergence of the approximated solutions generated by the Lax-Friedrichs scheme.

MSC:

35L65 Hyperbolic conservation laws
74B20 Nonlinear elasticity
35A35 Theoretical approximation in context of PDEs
35B25 Singular perturbations in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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