For a class of systems of nonlinear and nonlocal balance laws in several
space dimensions, we prove the local in time existence of solutions and their
continuous dependence on the initial datum. The choice of this class is
motivated by a new model devoted to the description of a metal plate being cut
by a laser beam. Using realistic parameters, solutions to this model obtained
through numerical integrations meet qualitative properties of real cuts.
Moreover, the class of equations considered comprises a model describing the
dynamics of solid particles along a conveyor belt