4 papers
On the Optimal Control Problem of Stochastic Semilinear Partial Differential Equations with Non-Globally Lipschitz Coefficients
Oleksiy Kapustyan, Olha Martynyuk, Oleksandr Misiats +1
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 boun…
Long Time Behavior of Stochastic Thin Film Equation
Oleksiy Kapustyan, Olha Martynyuk, Oleksandr Misiats +1
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…
Long Time Behavior of Stochastic Thin Film Equation
Oleksiy Kapustyan, Olha Martynyuk, Oleksandr Misiats +1
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 solu…
Thin Film Equations with Nonlinear Deterministic and Stochastic Perturbations
Oleksiy Kapustyan, Olha Martynyuk, Oleksandr Misiats +1
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 Trot…