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<p>We derive stochastic equations to describe reflected diffusion processes associated with the Cauchy–Neumann problem for systems of nonlinear parabolic equations in nondivergent form. The construction of a solution of the arisen stochastic problem is based on a localization procedure that allows reducing the problem in a closed domain to the corresponding problem in the half-space. As a result, we obtain a probabilistic representation of a weak solution of the Cauchy–Neumann problem in a bounded domain with a smooth boundary. Bibliography: 13 titles.</p>

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STOCHASTIC MODEL OF THE CAUCHY–ROBIN PROBLEM FOR SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Ya. I. Belopolskaya

摘要

We derive stochastic equations to describe reflected diffusion processes associated with the Cauchy–Neumann problem for systems of nonlinear parabolic equations in nondivergent form. The construction of a solution of the arisen stochastic problem is based on a localization procedure that allows reducing the problem in a closed domain to the corresponding problem in the half-space. As a result, we obtain a probabilistic representation of a weak solution of the Cauchy–Neumann problem in a bounded domain with a smooth boundary. Bibliography: 13 titles.