Geodesic
Generalized solutions of nonlinear parabolic systems and vanishing viscosity method
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 7-39

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In this paper we construct stochastic processes associated with nonlinear parablic equations and systems that allow to derive a probabilistic representation of a generalized solution to the Cauchy problem for them. We show also that in some cases the derived representation can be used to construct and investigate a smooth solution to the Cauchy problem for a hyperbolic system within the framework of the vanishing viscosity method. 
@article{ZNSL_2004_311_a0,
     author = {Ya. I. Belopol'skaya},
     title = {Generalized solutions of nonlinear parabolic systems and vanishing viscosity method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--39},
     publisher = {mathdoc},
     volume = {311},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a0/}
}
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Ya. I. Belopol'skaya. Generalized solutions of nonlinear parabolic systems and vanishing viscosity method. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 7-39. http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a0/