arXiv subjects

Olha Martynyuk

Publications and source records attributed to Olha Martynyuk.

5 recordsLinked to original sources

arXiv2026

On the Optimal Control Problem of Stochastic Semilinear Partial Differential Equations with Non-Globally Lipschitz Coefficients

In this paper, we study optimal control problems for stochastic semilinear partial differential equations, which lack the maximum principle, and whose coefficients do not have bounded Frechet derivatives. We propose an approximation scheme for the corresponding optimization problem, and prove convergence of the approximating solutions on both finite and infinite time intervals.

math.AP↗

arXiv2026

Long Time Behavior of Stochastic Thin Film Equation

We consider the stochastic thin-film equation with linear deterministic and stochastic Itô perturbations. The existence of nonnegative weak martingale solutions on the semi-axis is established, and their asymptotic behavior as $t \to \infty$ is investigated. It is shown that in square mean the $L^\infty$ norm of the solution converges to the spatial mean value of the initial condition, multiplied by a random factor similar to a geometric Wiener process.

math.AP↗

arXiv2025

On existence and continuation of mild solutions of functional-differential equations of neutral type in Banach spaces

The aim of this work is to investigate the conditions for the existence and continuation of a mild solution to the initial value problem of functional-differential equations of neutral type in Banach spaces to the boundary of the domain. Based on the Schauder fixed point theorem, the existence and continuation to the boundary of the domain are proved.

math.AP↗

arXiv2023

Long Time Behavior of Stochastic Thin Film Equation

In this paper we consider a stochastic thin-film equation with a one dimensional Gaussian Stratonovych noise. We establish the existence of non-negative global weak martingale solution, and study its long time asymptotic properties. In particular, we show the solution almost surely converges to the average value of the initial condition. Furthermore, using the regularized equations and adapted entropy functionals, we establish the exponential asymptotic decay of the solution in the uniform norm.

math.AP↗

arXiv2023

Thin Film Equations with Nonlinear Deterministic and Stochastic Perturbations

In this paper we consider stochastic thin-film equation with nonlinear drift terms, colored Gaussian Stratonovych noise, as well as nonlinear colored Wiener noise. By means of Trotter-Kato-type decomposition into deterministic and stochastic parts, we couple both of these dynamics via a discrete-in-time scheme, and establish its convergence to a non-negative weak martingale solution.

math.AP↗