15 citations · 47 across the 11 of their papers we have counts for
14 papers
Composite solutions to a liquid bilayer model
Georgy Kitavtsev
This article continues the research initiated in [17]. We derive explicit formulae for the leading order profiles of eleven types of stationary solutions to a one-dimensional two-l…
Asymptotic decay towards steady states of solutions to very fast and singular diffusion equations
Georgy Kitavtsev, Roman M. Taranets
We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having nonhomogeneous in space and time source…
Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics
Georgy Kitavtsev, Roman M. Taranets
In this paper, we extend the results of [1] by proving exponential asymptotic -convergence of solutions to a one-dimensional singular heat equation with -source term that…
Asymptotic decay and non-rupture of viscous sheets
Marco A. Fontelos, G. Kitavtsev, R. M. Taranets
For a nonlinear system of coupled PDEs, that describes evolution of a viscous thin liquid sheet and takes account of surface tension at the free surface, we show exponential $(H^1,…
Thin film models for active gels
Georgy Kitavtsev, Andreas Münch, Barbara Wagner
In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributi…
A Compactness and Structure Result for a Discrete Multi-Well Problem with Symmetry in Arbitrary Dimension
Georgy Kitavtsev, Gianluca Lauteri, Stephan Luckhaus +1
In this note we combine the "spin-argument" from [KLR15] and the -dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactne…
Thermal rupture of a free liquid sheet
Georgy Kitavtsev, Marco A. Fontelos, Jens Eggers
We consider a free liquid sheet, taking into account the dependence of surface tension on temperature, or concentration of some pollutant. The sheet dynamics are described within a…
Liquid crystal defects in the Landau-de Gennes theory in two dimensions-beyond the one-constant approximation
Georgy Kitavtsev, Jonathan M Robbins, Valeriy Slastikov +1
We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general -radially symmetric boundary conditions. We show that for generic elas…
Surface Energies Emerging in a Microscopic, Two-Dimensional Two-Well Problem
Georgy Kitavtsev, Stephan Luckhaus, Angkana Rüland
In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional)…
Surface Energies Arising in Microscopic Modeling of Martensitic Transformations
Georgy Kitavtsev, Stephan Luckhaus, Angkana Rüland
In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic lattice. The two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins, r…
Weak solutions to lubrication systems describing the evolution of bilayer thin films
Sebastian Jachalski, Georgy Kitavtsev, Roman Taranets
The existence of global nonnegative weak solutions is proved for coupled one-dimensional lubrication systems that describe the evolution of nanoscopic bilayer thin polymer films th…
Stationary solutions of liquid two-layer thin film models
Sebastian Jachalski, Robert Huth, Georgy Kitavtsev +2
We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to ach…
Coarsening rates for the dynamics of slipping droplets
Georgy Kitavtsev
We derive reduced finite dimensional ODE models starting from one dimensional lubrication equations describing coarsening dynamics of droplets in nanometric polymer film interactin…
Weak solutions to lubrication equations in the presence of strong slippage
Georgy Kitavtsev, Philippe Laurencot, Barbara Niethammer
The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hydrophobyzed substr…