3 citations · 3 across the 5 of their papers we have counts for
6 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…
Strong solutions and asymptotic behavior of bidomain equations with random noise
Oleksiy Kapustyan, Oleksandr Misiats, Oleksandr Stanzhytskyi
In this paper we study the conditions for the existence of strong solutions (both local and global) for stochastic bidomain equations. To this end, we use apriori energy estimates…
Well-posedness and robust stability of a nonlinear ODE-PDE system
S. Dashkovskiy, O. Kapustyan, V. Slynko
This work studies stability and robustness of a nonlinear system given as an interconnection of an ODE and a parabolic PDE subjected to external disturbances entering through the b…