Physics – Mathematical Physics
Scientific paper
2011-01-30
Physics
Mathematical Physics
18 pages
Scientific paper
We introduce integral identities to define delta-shock wave type solutions for the multidimensional zero-pressure gas dynamics Using these integral identities, the Rankine-Hugoniot conditions for delta-shocks are obtained. We derive the balance laws describing mass, momentum, and energy transport from the area outside the delta-shock wave front onto this front. These processes are going on in such a way that the total mass, momentum, and energy are conserved and at the same time mass and energy of the moving delta-shock wave front are increasing quantities. In addition, the total kinetic energy transfers into the total internal energy. The process of propagation of delta-shock waves is also described. These results can be used in modeling of mediums which can be treated as a {pressureless continuum} (dusty gases, two-phase flows with solid particles or droplets, granular gases).
Albeverio Sergio
Rozanova Olga S.
Shelkovich V. M.
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