51 citations · 92 across the 14 of their papers we have counts for
16 papers
Malliavin Calculus for the one-dimensional Stochastic Stefan Problem
Dimitra C. Antonopoulou, Dimitrios Dimitriou, Georgia Karali +1
We consider the one-dimensional outer stochastic Stefan problem with reflection. The problem admits maximal solutions as long as the velocity of the moving boundary remains bounded…
Existence of maximal solutions for the financial stochastic Stefan problem of a volatile asset with spread
D. C. Antonopoulou, D. Farazakis, G. Karali
In this work, we consider the outer Stefan problem for the short-time prediction of the spread of a volatile asset traded in a financial market. The stochastic equation for the evo…
Layer dynamics for the one dimensional -dependent Cahn-Hilliard / Allen-Cahn equation
Dimitra Antonopoulou, Georgia Karali, Konstantinos Tzirakis
We study the dynamics of the one-dimensional -dependent Cahn-Hilliard / Allen-Cahn equation within a neighborhood of an equilibrium of transition layers, that in g…
The multi-dimensional Stochastic Stefan Financial Model for a portfolio of assets
Dimitra C. Antonopoulou, Marina Bitsaki, Georgia Karali
The financial model proposed involves the liquidation process of a portfolio of assets through sell or (and) buy orders with volatility. We present the rigorous mathematical fo…
Numerical approximation of the Stochastic Cahn-Hilliard Equation near the Sharp Interface Limit
Dimitra Antonopoulou, Lubomir Banas, Robert Nürnberg +1
We consider the stochastic Cahn-Hilliard equation with additive noise term () that scales with the interfacial width parameter . We ver…
Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation
Matthieu Alfaro, Dimitra Antonopoulou, Georgia Karali +1
We study an $\ep$-dependent stochastic Allen--Cahn equation with a mild random noise on a bounded domain in , . Here $\ep$ is a small positive parameter that…
Malliavin calculus for the stochastic Cahn-Hilliard / Allen Cahn equation with unbounded noise diffusion
D. C. Antonopoulou, D. Farazakis, G. D. Karali
The stochastic partial differential equation analyzed in this work, is motivated by a simplified mesoscopic physical model for phase separation. It describes pattern formation due…
On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS equation on the Half-Line; Zero Initial Data
Dimitra C. Antonopoulou, Spyridon Kamvissis
Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his c…
On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS equation on the Half-Line; Non-zero Initial Data
Dimitra C. Antonopoulou, Spyridon Kamvissis
Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his c…
The Sharp interface limit for the stochastic Cahn-Hilliard equation
Dimitra C. Antonopoulou, Dirk Blömker, Georgia D. Karali
We study the two and three dimensional stochastic Cahn-Hilliard equation in the sharp interface limit, where the positive parameter tends to zero, which measures the width of t…
Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation
Dimitra C. Antonopoulou, Peter W. Bates, Dirk Blömker +1
We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with…
Existence and regularity of solution for a Stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion
Dimitra C. Antonopoulou, Geogia Karali, Annie Millet
The Cahn-Hilliard/Allen-Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms…
A Hilbert expansions method for the rigorous sharp interface limit of the generalized Cahn-Hilliard Equation
D. C. Antonopoulou, G. D. Karali, E. Orlandi
We consider Cahn-Hilliard equations with external forcing terms. Energy decreasing and mass conservation might not hold. We show that level surfaces of the solutions of such genera…
Crank-Nicolson Finite Element Discretizations for a 2D Linear Schrödinger-Type Equation Posed in a Noncylindrical Domain
D. C. Antonopoulou, G. D. Karali, M. Plexousakis +1
Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, w…
A Finite Difference method for the Wide-Angle `Parabolic' equation in a waveguide with downsloping bottom
D. C. Antonopoulou, V. A. Dougalis, G. E. Zouraris
We consider the third-order wide-angle `parabolic' equation of underwater acoustics in a cylindrically symmetric fluid medium over a bottom of range-dependent bathymetry. It is kno…
Galerkin Methods for Parabolic and SCHR{Ö}DINGER Equations with Dynamical Boundary Conditions and Applications to Underwater Acoustics
D. C. Antonopoulou, V. A. Dougalis, G. E. Zouraris
In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schrödinger evo…