2 citations · 5 across the 13 of their papers we have counts for
15 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 a nonlocal and non-monotone SPDE-ODE system arising in electrophysiology
Tobias Gebäck, Oleksandr Misiats, Ioanna Motschan Ulander +1
This paper concerns a coupled semilinear SPDE-ODE system modelling the electropermeabilization phenomenon, which designates a transient increase in cell membrane permeability induc…
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…
An energy minimization approach to twinning with variable volume fraction
Sergio Conti, Robert Kohn, Oleksandr Misiats
In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example…
Invariant Measure for Neutral Stochastic Functional Differential Equations with Non-Lipschitz Coefficients
Andriy Stanzhytskyi, Oleksandr Stanzhytskyi, Oleksandr Misiats
In this work we study the long time behavior of nonlinear stochastic functional-differential equations of neutral type in Hilbert spaces with non-Lipschitz nonlinearities. We estab…
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…
On global existence and blowup of solutions of stochastic Keller-Segel type equation
Oleksandr Misiats, Oleksandr Stanzhytskyi, Ihsan Topaloglu
In this paper we consider a stochastic Keller-Segel type equation, perturbed with random noise. We establish that for special types of random pertubations (i.e. in a divergence for…
Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces
Oleksandr Misiats, Viktoriia Mogylova, Oleksandr Stanzhytskyi
In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence an…
On minimizers of an anisotropic liquid drop model
Oleksandr Misiats, Ihsan Topaloglu
We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes ar…
Singular perturbation of an elastic energy with a singular weight
Oleksandr Misiats, Ihsan Topaloglu, Daniel Vasiliu
We study the singular perturbation of an elastic energy with a singular weight. The minimization of this energy results in a multi-scale pattern formation. We derive an energy scal…
Convergence of Space-Time Discrete Threshold Dynamics to Anisotropic Motion by Mean Curvature
Oleksandr Misiats, Nung Kwan Yip
We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be v…
Existence and uniqueness of invariant measures for stochastic reaction-diffusion equations in unbounded domains
Oleksandr Misiats, Oleksandr Stanzhytsyi, Nung Kwan Yip
In this paper we investigate the long-time behavior of stochastic reaction-diffusion equations of the type , where is an elliptic operator, …
Ginzburg-Landau model with small pinning domains
Mickaël Dos Santos, Oleksandr Misiats
We consider a Ginzburg-Landau type energy with a piecewise constant pinning term in the potential . The function is different from 1 only on finitely many…