Singular and selfsimilar solutions for Euler equations with phase transitions (Q504631)

The authors discuss the following equations for the density \(\rho\), the velocity \(v\) and the specific total energy \(E\): \(\frac{\partial \rho}{\partial t}+ \frac{\partial (\rho v)}{\partial x} = 0\), \( \frac{\partial (\rho v)}{\partial t} + \frac{\partial (\rho v^2+\rho)}{\partial x}= 0\), \( \frac{\partial (\rho E)}{\partial t} + \frac{\partial (\rho E v+\rho v)}{\partial x}= 0\) with three discontinuity conditions. One of the typical condition at a point has the form \(\frac{d}{dt} \rho_s -[\dot{m}] =0\) where \([\dot{m}]\) denotes the jump of the considered function. The authors construct self-similar as well as singular solutions of the problem and describe their structure.