5 papers
On approximation of Ginzburg-Landau minimizers by -valued maps in domains with vanishingly small holes
Leonid Berlyand, Dmitry Golovaty, Oleksandr Iaroshenko +1
We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between…
Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit
Leonid Berlyand, Mykhailo Potomkin, Volodymyr Rybalko
This letter is concerned with asymptotic analysis of a PDE model for motility of a eukaryotic cell on a substrate. This model was introduced in [1], where it was shown numerically…
Singularly perturbed spectral problems with Neumann boundary conditions
A. Piatnitski, A. Rybalko, V. Rybalko
The paper deals with the Neumann spectral problem for a singularly perturbed second order elliptic operator with bounded lower order terms. The main goal is to provide a refined de…
Solutions with Vortices of a Semi-Stiff Boundary Value Problem for the Ginzburg-Landau Equation
L. Berlyand, V. Rybalko
We study solutions of the 2D Ginzburg-Landau equation -Δu+\frac{1}{\ve^2}u(|u|^2-1)=0 subject to "semi-stiff" boundary conditions: the Dirichlet condition for the modulus, |u|=1, a…
Capacity of a multiply-connected domain and nonexistence of Ginzburg-Landau minimizers with prescribed degrees on the boundary
Leonid Berlyand, Dmitry Golovaty, Volodymyr Rybalko
Suppose that . In the annular domain we consider the class of complex valued maps having degree 1 on and on .…