8 papers · 1 filter
Emergence of traveling waves and their stability in a free boundary model of cell motility
Volodymyr Rybalko, Leonid Berlyand
We introduce a two-dimensional Hele-Shaw type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped…
Stability of steady states and bifurcation to traveling waves in a free boundary model of cell motility
Leonid Berlyand, Volodymyr Rybalko
We introduce a two-dimensional Keller-Segel type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdam…
Derivation of cable equation by multiscale analysis for a model of myelinated axons
Carlos Jerez-Hanckes, Irina Pettersson, Volodymyr Rybalko
The paper concerns the multiscale modeling of a myelinated axon. Taking into account the microstructure with alternating myelinated parts and nodes Ranvier, we derive a nonlinear c…
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…