Convergence of the Viscosity Solutions for the System of Nonlinear Elasticity*

In this paper some special entropy pairs of Lax type are constructed for the system of nonlinear elasticity, in which the progressive terms are functions of a single variable. The necessity estimates for the major terms are obtained by using the theory of singular perturbation of the ordinary differential equations. The special entropy pairs are used to prove that the family of Young measures uniquely determined by the viscosity solution sequence is a family of Dirac measures. Hence, a convergence theorem on the viscosity solutions is established by applying the method of compensated compactness