One-dimensional Riemann problem for equations of constant pressure fluid dynamics with measure solutions by the viscosity method

摘要

The Riemann problem for the equations of constant pressure fluid dynamics was considered. Solutions of this problem were constructed by employing the viscosity vanishing approach. For some initial data, solutions can be viewed as bounded functions in L-infinity(R x R+) plus bounded linear functionals on C-0(infinity)(R x R+) with nonclassical waves as their supports. Vacuum regions appear so that uniqueness of Riemann solutions fails for some initial data. Mathematics Subject Classification (1991): 35L65. [References: 22]