On one combinatorial lemmaProceedings of the Steklov Institute of Mathematics - Tập 272 - Trang 186-196 - 2011
Yu. A. Shashkin
We study n-dimensional cubical pseudomanifolds and their cellular mappings. In particular, we consider a discrete n-cube and all of its (n − 1)-faces. Then, there exist either one or two or four faces of the cube each of which is mapped onto one face.
Protter-Morawetz multidimensional problemsProceedings of the Steklov Institute of Mathematics - Tập 278 - Trang 179-198 - 2012
Nedyu Popivanov, Todor Popov, Rudolf Scherer
About 50 years ago M.H. Protter introduced boundary value problems that are multidimensional analogues of the classical plane Morawetz problems for equations of mixed hyperbolic-elliptic type that model transonic fluid flows. Up to now there are no general existence results for the Protter-Morawetz multidimensional problems, and an understanding of the situation is not at hand. At the same time, P...... hiện toàn bộ
Global Meromorphy of Solutions of the Painlevé Equations and Their HierarchiesProceedings of the Steklov Institute of Mathematics - Tập 311 - Trang 98-113 - 2021
A. V. Domrin, B. I. Suleimanov, M. A. Shumkin
We show that all local holomorphic solutions of all equations constituting the hierarchies of the first and second Painlevé equations can be analytically continued to meromorphic functions on the whole complex plane. We also present a new conceptual proof of the fact that all local holomorphic solutions of the first, second, and fourth Painlevé equations are globally meromorphic.
On a nonstationary problem of group pursuitProceedings of the Steklov Institute of Mathematics - Tập 271 - Trang 41-52 - 2011
A. S. Bannikov, N. N. Petrov
Pontryagin’s classical nonstationary example with many participants and phase constraints on the evader’s states with equal dynamic and inertia capabilities of the players is considered. The case of a simple motion is considered separately. Solvability conditions for problems of pursuit and evasion are obtained.
Singularities of elliptic mixed boundary problems. Application to boundary stabilization of hyperbolic systemsProceedings of the Steklov Institute of Mathematics - Tập 270 - Trang 172-183 - 2010
J. -P. Lohéac
For elliptic partial differential equations, mixed boundary conditions generate singularities in the solution, mainly when the boundary of the domain is connected. We here consider two classical cases: the Laplace equation and the Lamé system. The knowledge of singularities allows us to construct adapted Rellich relations. These are useful in the problem of boundary stabilization of the wave equat...... hiện toàn bộ
Nonstationary solutions of a generalized Korteweg-de Vries-Burgers equationProceedings of the Steklov Institute of Mathematics - Tập 281 - Trang 204-212 - 2013
A. P. Chugainova
Nonstationary solutions of the Cauchy problem are found for a model equation that includes complicated nonlinearity, dispersion, and dissipation terms and can describe the propagation of nonlinear longitudinal waves in rods. Earlier, within this model, complex behavior of traveling waves has been revealed; it can be regarded as discontinuity structures in solutions of the same equation that ignore...... hiện toàn bộ
The Peano-Baker seriesProceedings of the Steklov Institute of Mathematics - Tập 275 - Trang 155-159 - 2012
Michael Baake, Ulrike Schlägel
This note reviews the Peano-Baker series and its use to solve the general linear system of ODEs. The account is elementary and self-contained, and is meant as a pedagogic introduction to this approach, which is well known but usually treated as a folklore result or as a purely formal tool. Here, a simple convergence result is given, and two examples illustrate that the series can be used explicitl...... hiện toàn bộ