Generalized Solutions of Nonlinear Parabolic Systems and the Vanishing Viscosity Method
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We show in this paper that stochastic processes associated with nonlinear parabolic equations and systems allow one to construct a probabilistic representation of a generalized solution to the Cauchy problem. We also show that in some cases the derived representation can be used to construct a solution to the Cauchy problem for a hyperbolic system via the vanishing viscosity method. Bibliography: 12 titles.
KeywordsViscosity Stochastic Process Generalize Solution Cauchy Problem Probabilistic Representation
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