English

Transport and concentration processes in the multidimensional zero-pressure gas dynamics model with the energy conservation law

Mathematical Physics 2011-02-01 v1 Analysis of PDEs math.MP

Abstract

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).

Keywords

Cite

@article{arxiv.1101.5815,
  title  = {Transport and concentration processes in the multidimensional zero-pressure gas dynamics model with the energy conservation law},
  author = {S. Albeverio and O. S. Rozanova and V. M. Shelkovich},
  journal= {arXiv preprint arXiv:1101.5815},
  year   = {2011}
}

Comments

18 pages