Generalized solutions of nonlinear parabolic systems and vanishing viscosity method

In this paper we construct stochastic processes associated with nonlinear parablic equations and systems that allow to derive a probabilistic representation of a generalized solution to the Cauchy problem for them. We show also that in some cases the derived representation can be used to construct and investigate a smooth solution to the Cauchy problem for a hyperbolic system within the framework of the vanishing viscosity method.