Abstract:
We construct a probabilistic representation of the Cauchy problem
solution for a system of nonlinear parabolic equations and give
the conditions which guarantee that this representation can be
applied to construct and investigate a solution of the Cauchy
problem for a system of nonlinear hyperbolic equations. As an
example, we consider the system of gas dynamic equations and its
parabolic regularization.
Keywords:diffusion processes, multiplicative operator functionals, systems of nonlinear parabolic and hyperbolic equations, vanishing viscosity methodž.
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