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Journal of Mathematical Sciences

, Volume 133, Issue 3, pp 1207–1223 | Cite as

Generalized Solutions of Nonlinear Parabolic Systems and the Vanishing Viscosity Method

  • Ya. I. Belopolskaya
Article

Abstract

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.

Keywords

Viscosity Stochastic Process Generalize Solution Cauchy Problem Probabilistic Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Ya. I. Belopolskaya
    • 1
  1. 1.St.Petersburg University for Architecture and Civil EngineeringSt.PetersburgRussia

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