Probabilistic representation of a generalized solution to the Cauchy problem for a PDE system with cross-diffusion

摘要

In this paper we derive a system of stochastic differential equations associated with a fully nondiagonal system of quasilinear parabolic equations. We construct a probabilistic representation of a generalized solution to the Cauchy problem for a cross-diffusion system in terms of averages over trajectories of solution of the derived stochastic system.