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The asymptotic expressions are given for the solution at a shock-generation point, a shock-interaction point, and at the time infinity to develop a quantitative statement about the shock wave. The formula by Lax (1957, 1973) is employed to demonstrate the determination of the shock-point location and the behavior of the solution at the point of discontinuity. Asymptotic expansions are developed that provide the shock curve and the entropy solution at the shock-generation point, and the method is applied to cases related to specific shock-interaction times or cases with initial data characterized by compact support. 8 refs.

Asymptotic formulas for the shock wave of the scalar conservation law with smooth initial data