Igor Lobanov

Numerical approach to the Stokes problem with high contrasts in viscosity

Abstract An algorithm based on Sherman–Morrison–Woodbury formula to solve numerically the Stokes problem is described. The algorithm allows to obtain the solution for viscosity contrasts up to ten orders of magnitude, moreover solution speed does not depend on viscosity contrast. Tests of accuracy of the algorithm are provided.

Two particle scattering on pencil of rays

We consider the scattering problem for the two particle Schroodinger operator on the star graph, which can be considered as an explicitly solvable model of the many electron Hamiltonian on a nanotubes junction. For inverse square interaction potential, the Green function and the scattering matrix are obtained.

Approximation of point perturbations on finite set of Laplace-Beltrami operator on Riemannian manifold

The work is devoted to the substantiation of zero-range potentials in case of nontrivial geometry. We bind two approaches to point perturbations: restriction-extension and approximation by family of Schrodinger operators with regular potentials.