Resumen de Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes

Ya. Belopolskaya, W. A. Woyczynski

• We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.