Convergence of the viscosity solutions for the system of nonlinear elasticity. (English) Zbl 0879.73013
Summary: Special entropy pairs of Lax type are constructed for the system of nonlinear elasticity, in which the main terms are functions of a single variable. Some estimates for these terms are obtained by using the theory of singular perturbation of ordinary differential equations. The special entropy pairs are used to prove that the family of Young measures, uniquely determined by a sequence of viscosity solutions, is a family of Dirac measures. Finally, a convergence theorem for the viscosity solutions is established by applying the method of compensated compactness.
MSC:
| 74B20 | Nonlinear elasticity |
| 35Q72 | Other PDE from mechanics (MSC2000) |
Keywords:
entropy pairs of Lax type; theory of singular perturbation; family of Young measures; family of Dirac measures; method of compensated compactnessReferences:
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