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A STOCHASTIC APPROACH TO THE CAUCHY-NEUMANN PROBLEM FOR SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS

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Abstract

We derive stochastic equations to describe reflected diffusion processes associated with the Cauchy-Neumann problem for systems of nonlinear parabolic equations in non-divergent form in the half-space. As a result, we obtain probabilistic representations of weak solutions to this problem.

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Acknowledgements

The author certifies that she has no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The author has no financial or proprietary interests in any material discussed in this article.

Funding

The work was supported by the RSF Grant 22-21-00016. The work was partially supported by Sirius University of Science and Technology, Russia.

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  1. Sirius University, Olympic prosp., 1, 354340, Sochi, Russia

    Ya. I. Belopolskaya

  2. St. Petersburg Department of V.A. Steklov Mathematical Institute, 27 Fontanka St, 191023, St Petersburg, Russia

    Ya. I. Belopolskaya

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Correspondence to Ya. I. Belopolskaya.

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Belopolskaya, Y. A STOCHASTIC APPROACH TO THE CAUCHY-NEUMANN PROBLEM FOR SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS. J Math Sci 266, 832–848 (2022). https://doi.org/10.1007/s10958-022-06119-w

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  • DOI: https://doi.org/10.1007/s10958-022-06119-w

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