Radially symmetric shadow wave solutions to the system of pressureless   gas dynamics in arbitrary dimensions
  Radially symmetric shadow wave solutions to the system of multidimensional pressureless gas dynamics are introduced, which allow one to capture concentration of mass. The transformation to a one-dimensional system with source terms is performed and physically meaningful boundary conditions at the origin are determined. Entropy conditions are derived and applied to single out physical (nonnegative mass) and dissipative (entropic) solutions. A complete solution to the pseudo-Riemann problem with initial data exhibiting a single shock on a sphere is obtained. 
Marko Nedeljkov, Lukas Neumann, Michael Oberguggenberger, Manas Sahoo
math.AP