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- D. C. Antonopoulou, V. A. Dougalis, Georgios E. Zouraris
- SIAM J. Numerical Analysis
- 2009

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 evolution equations with dynamical boundary conditions. Error estimates of optimal rates of convergence in L 2 and H 1 are proved for the accociated semidiscrete and fully discrete… (More)

- D. C. Antonopoulou, M. Plexousakis
- Numerische Mathematik
- 2010

- D. C. Antonopoulou, Dirk Blömker, Georgia D. Karali
- SIAM J. Math. Analysis
- 2012

We describe the joint motion of multiple kinks or interfaces for the one-dimensional Cahn-Hilliard equation on a bounded interval perturbed by small additive noise The approach is based on an approximate slow manifold, where the motion of interfaces are described by the projection onto the manifold. This was used by Bates and Xun (1994/95) to verify… (More)

- D. C. Antonopoulou, P. W. Bates, Dirk Blömker, Georgia D. Karali
- SIAM J. Math. Analysis
- 2016

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, we analyze a general Schrödinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initial-and boundary-value problem is… (More)

The standard 'parabolic' approximation to the Helmholtz equation is used in order to model long-range propagation of sound in the sea in the presence of cylindrical symmetry in a domain with a rigid bottom of variable topography. The rigid bottom is modeled by a homogeneous Neumann condition and a paraxial approximation thereof proposed by Abrahamsson and… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a r t i c l e i n f o a b s t r a c t Ostwald ripening is the coarsening phenomenon… (More)

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 collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the… (More)

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 in the context of surface processes. For such an equation we consider a multiplicative space-time white noise with diffusion coefficient of sub-linear growth. Using technics from… (More)

- D. C. Antonopoulou, Georgia D. Karali
- NHM
- 2013

We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polar coordinates. Furthermore, we construct finite difference numerical schemes and present numerical results for the evolution of non-convex closed plane curves under this… (More)