Generalized Solutions of Nonlinear Parabolic Systems and the Vanishing Viscosity Method

We show in this paper that stochastic processes associated with nonlinear parabolic equations and systems allow one to construct a probabilistic representation of a generalized solution to the Cauchy problem. We also show that in some cases the derived representation can be used to construct a solution to the Cauchy problem for a hyperbolic system via the vanishing viscosity method. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 7–39.