Abstract
The purpose of this paper is to construct both strong and weak solutions (in certain functional classes) of the Cauchy problem for a class of systems of nonlinear parabolic equations via a unified stochastic approach. To this end we give a stochastic interpretation of such a system, treating it as a version of the backward Kolmogorov equation for a two-component Markov process with coefficients depending on the distribution of its first component. To extend this approach and apply it to the construction of a generalized solution of a system of nonlinear parabolic equations, we use results from Kunita's theory of stochastic flows.
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