Ya. I. Belopolskaya, “Stochastic model of the Cauchy–Neumann problem for nonlinear parabolic equations”, Zap. Nauchn. Sem. POMI, 2021, Volume 505,Pages <nobr>38

This article is cited in 1 paper

Stochastic model of the Cauchy–Neumann problem for nonlinear parabolic equations

Ya. I. Belopolskaya^ab

^a University of Science and Technology "Sirius", Sochi
^b St. Petersburg State University of Architecture and Civil Engineering

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

Key words and phrases: stochastic models, reflected diffusion, Skorokhod's problem, weak solutions of the Cauchy–Neumann problem.

UDC: 519.2

Received: 15.11.2021