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A Probability Approach to the Method of Vanishing Viscosity

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Abstract

We clarify conditions under which solutions to the Cauchy problem for a general (fully nondiagonal) system of linear and nonlinear parabolic equations admit probability representations. Such representations are also used for constructing and studying solutions to the Cauchy problem for nonlinear hyperbolic systems. Bibliography: 26 titles.

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  1. Ya. I. Belopol'skaya
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Belopol'skaya, Y.I. A Probability Approach to the Method of Vanishing Viscosity. Journal of Mathematical Sciences 120, 1051–1079 (2004). https://doi.org/10.1023/B:JOTH.0000014836.58121.fa

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  • DOI: https://doi.org/10.1023/B:JOTH.0000014836.58121.fa

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