Abstract:
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
finally get the existence and the stability of solutions.