CONVERGENCE OF THE VISCOSITY SOLUTIONS FOR THE SYSTEM OF NONLINEAR ELASTICITY

In this paper some special entropy pairs of Lax type are constructed f or the system of nonlinear elasticity, in which the progressive terms are functions of a single variable. The necessity estimates for the ma jor terms are obtained by using the theory of singular perturbation of the, ordinary differential equations. The special entropy pairs are u sed 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 app lying the method of compensated compactness. (C) 1997 Academic Press.