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Probabilistic representation of a generalized solution to the Cauchy problem for a PDE system with cross-diffusion

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Abstract

In this paper we derive a system of stochastic differential equations associated with a fully nondiagonal system of quasilinear parabolic equations. We construct a probabilistic representation of a generalized solution to the Cauchy problem for a cross-diffusion system in terms of averages over trajectories of solution of the derived stochastic system.

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Authors and Affiliations

  1. St. Petersburg State University for Architecture and Civil Engineering, St. Petersburg, Russia

    Ya. I. Belopolskaya

Authors
  1. Ya. I. Belopolskaya
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Correspondence to Ya. I. Belopolskaya.

Additional information

Original Russian Text © Ya.I. Belopolskaya, 2015, published in Doklady Akademii Nauk, 2015, Vol. 461, No. 1, pp. 10–13.

The article was translated by the author.

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Belopolskaya, Y.I. Probabilistic representation of a generalized solution to the Cauchy problem for a PDE system with cross-diffusion. Dokl. Math. 91, 134–137 (2015). https://doi.org/10.1134/S1064562415020027

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  • DOI: https://doi.org/10.1134/S1064562415020027

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