Probabilistic Representations and Numerical Algorithms for Classical and Viscosity Solutions of the Cauchy Problem for Quasilinear Parabolic Systems

Abstract

We propose two approaches which allow us to construct probabilistic representations of classical and viscosity solutions of the Cauchy problem for a system of quasilinear parabolic equations. Based on these representations, we develop two numerical algorithms to construct the required solution. The system under consideration arises as a mathematical model of parabolic conservation laws. Bibliography: 14 titles.