Abstract
The aim of this paper is to extend to multidimensions the study of a pressureless model of a gas system with unilateral constraint. Several difficulties are added with respect to the one-dimensional case. Indeed the geometry of the dynamics of blocks cannot be conserved and to solve this problem, we approximate the motion of each block by discrete jumps in all the directions separately in consecutive time steps. This leads to approximations of solutions for special initial data. Then the stability of these approximations has to be adapted to this new situation. We finally get the existence and the stability of solutions.
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