  We introduce a new class of nonlinear Stochastic Differential Equations in
the sense of McKean, related to non conservative nonlinear Partial Differential
equations (PDEs). We discuss existence and uniqueness pathwise and in law under
various assumptions. We propose an original interacting particle system for
which we discuss the propagation of chaos. To this system, we associate a
random function which is proved to converge to a solution of a regularized
version of PDE.
