Proceedings of the Steklov Institute of Mathematics

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Jacob’s ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations
Proceedings of the Steklov Institute of Mathematics - Tập 276 - Trang 208-221 - 2012
Jan Moser
In this paper we obtain new formulae for short and microscopic parts of the Hardy-Littlewood integral, and the first asymptotic formula for the sixth-order expression $$\left| {\zeta \left( {\tfrac{1} {2} + i\phi _1 \left( t \right)} \right)} \right|^4 \left| {\zeta \left( {\tfrac{1} {2} + it} \right)} \right|^2$$ ...... hiện toàn bộ
On one combinatorial lemma
Proceedings 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 problems
Proceedings 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 Hierarchies
Proceedings 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.
Reconstruction of boundary controls in parabolic systems
Proceedings of the Steklov Institute of Mathematics - Tập 280 Số S1 - Trang 98-118 - 2013
A. I. Korotkii, Дарья Олеговна Михайлова
On a nonstationary problem of group pursuit
Proceedings 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 systems
Proceedings 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 equation
Proceedings 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
Operator Estimates in Two-Dimensional Problems with a Frequent Alternation in the Case of Small Parts with the Dirichlet Condition
Proceedings of the Steklov Institute of Mathematics - Tập 321 - Trang S33-S52 - 2023
D. I. Borisov
A two-dimensional boundary value problem is studied for a general scalar elliptic second-order equation of the general form with frequent alternation of boundary conditions. The alternation is defined on small, closely spaced parts of the boundary on which the Dirichlet boundary condition and the nonlinear Robin boundary condition are set alternately. The distribution and size of these segments ar...... hiện toàn bộ
The Peano-Baker series
Proceedings 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
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