Geodesic
A probabilistic approach to a solution of nonlinear parabolic
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 625-652

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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.
Mots-clés : diffusion processes
Keywords: multiplicative operator functionals, systems of nonlinear parabolic and hyperbolic equations, vanishing viscosity methodю. 
@article{TVP_2004_49_4_a0,
     author = {Ya. I. Belopol'skaya},
     title = {A probabilistic approach to a solution of nonlinear parabolic},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {625--652},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a0/}
}
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Ya. I. Belopol'skaya. A probabilistic approach to a solution of nonlinear parabolic. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 625-652. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a0/