Seminar “On solutions to initial boundary value problems for the Kawahara equation and its generalizations”
The following presentation is devoted to the three problems for various modifications of the Kawahara equation. In the first part of the presentation, we consider the large time decay of solutions of the initial boundary value problem for the damped Kawahara equation.
Seminar “Solving the Vlasov equation using neural networks”
This work is devoted to the numerical solution of the Vlasov equation in one-dimensional case without electric field using neural networks.
Seminar “Mathematical modeling of EEG-dynamics”
In this work we model spatiotemporal dynamics in EEG data with the Poisson equation where the right-hand side corresponds to the oscillating brain sources.
Seminar: “Boundary regimes with peaking and large solutions of quasilinear parabolic equations”
There will be presented results on localized and non-localized boundary regimes with singular peaking in some finite time moment for general quasilinear parabolic equations.
Seminar “Modeling of the wave perturbation propagation in the heterogeneous environment using the grid-characteristic method”
This work is devoted to the development of numerical methods of higher order of accuracy and a software package for mathematical modeling of dynamic wave disturbances as applied to seismic, seismic exploration, geophysics, strength and nondestructive testing problems.
Scientific seminar “Supercomputer simulation of monatomic rarefied gas flows using parallel code “Nesvetay””
The presentations makes an overview of the current capabilities of the Nesvetay code as applied to monatomic rarefied gas flows based on the numerical solution of the kinetic equation with BGK and E.M. Shakhov (S-model) collision integrals. The “Nesvetay” code uses the author’s version of the discrete velocity method, which includes a finite volume scheme for approximating the transfer operator on arbitrary spatial grids, a conservative method for calculating macroparameters on an unstructured velocity grid, an implicit scheme for stationary problems, and an explicit method on moving deforming grids for modeling nonstationary currents.
Scientific seminar “Decomposition on the root vector series of the non-selfadjoint operators with the s-number asymptotics more subtle than one of the power type”
The first our aim is to clarify the results obtained by Lidskii V.B. devoted to the decomposition on the root vector system of a non-selfadjoint compact operator. We use a technique of the entire function theory and introduce a so-called Schatten-von Neumann class of the convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms of the norm, we construct a sequence of contours of the power type on the contrary to the results by Lidskii V.B., where a sequence of contours of the exponential type was used. This approach allows us to obtain a decomposition on the root vector series of the non-selfadjoint operators with the s-number asymptotics more subtle than one of the power type.