Probabilistic Approach to Systems of Nonlinear PDEs and Vanishing Viscosity Method
2006, v.12, Issue 1, 59-94
Conditions that ensure the possibility to use the probabilistic approach via vanishing viscosity method to study the Cauchy problem for hyperbolic systems are given. The probabilistic representation of the classical solution to the Cauchy problem for a nonlinear system of parabolic equations is used to study the smooth solution of the Cauchy problem for the correspondent limiting nonlinear hyperbolic system.
Keywords: diffusion processes,nonlinear hyperbolic and parabolicequations and systems,the Cauchy problem