Abstract
A notion of entropy quasisolution is introduced for the Euler equations of isothermal gas flows. Such a solution is obtained by means of nonlinear parabolic approximation with a small parameter ε. Compensated compactness argument is applied to justify the passage to limit as ε → 0 for the case when the mass density is strictly positive. It is verified that smooth entropy quasisolution is necessarily a classic solution. An example of entropy solution with a shock front is constructed to reveal that it is not an entropy quasisolution. The study is motivated by the explosion physics experiments in which the mass conservation law may be violated at a shock front passing through the gas.
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