GENERALIZED SOLUTIONS OF NONLINEAR PARABOLIC SYSTEMS AND THE VANISHING VISCOSITY METHOD

摘要

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 cas'es the derived representation can be used to construct a solution to the Cauchy problem for a hyperbolic system via the vanishing viscosity method.