Theoretical study of a multi-dimensional pressureless model with unilateral constraint

We extend to multi-dimension the study of a pressureless model of gas system with unilateral constraint. Several difficulties are added with respect to the one-dimensional case. First, the geometry of the dynamics of blocks cannot be conserved and to solve this problem, a splitting with respect to the various directions is done. This leads to approximations of solutions for special initial data. Besides, the stability of the solutions is also quite different from the one-dimensional case. We finaly get the existence and the stability of solutions.