Proceedings of the Steklov Institute of Mathematics
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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
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......
The Peano-Baker series
Proceedings of the Steklov Institute of Mathematics - Tập 275 - Trang 155-159 - 2012
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......
On the approximation of nonlinear conflict-controlled systems of neutral type
Proceedings of the Steklov Institute of Mathematics - Tập 292 - Trang 182-196 - 2016
We consider approximations of systems of nonlinear neutral-type equations in Hale’s form by systems of high-order ordinary differential equations. A procedure is given for the mutual feedback tracking between the motion of the original neutral-type conflict-controlled system and the motion of the approximating system of ordinary differential equations. The proposed mutual tracking procedure makes ......
Invariant planes, indices of inertia, and degrees of stability of linear dynamic equations
Proceedings of the Steklov Institute of Mathematics - Tập 258 - Trang 147-154 - 2007
Spectral properties of linear dynamic equations linearized at equilibrium points are analyzed. The analysis involves a search for invariant planes that are uniquely projected onto the configuration plane. In turn, the latter problem reduces to the solution of a quadratic matrix equation of special form. Under certain conditions, the existence of two different solutions is proved by the contraction......
On the multiplicity of solutions of a system of algebraic equations
Proceedings of the Steklov Institute of Mathematics - - 2012
Integral approximation of the characteristic function of an interval by trigonometric polynomials
Proceedings of the Steklov Institute of Mathematics - Tập 264 - Trang 19-38 - 2010
We prove that the value E
n−1(χ
h
)
L
of the best integral approximation of the characteristic function χ
h
of an interval (−h, h) on the period [−π,π) by trigonometric polynomials of degree at most n − 1 is expressed in t......
Reconstruction of external actions under incomplete information in a linear stochastic equation
Proceedings of the Steklov Institute of Mathematics - Tập 296 - Trang 196-205 - 2017
The problem of reconstructing unknown external actions in a linear stochastic differential equation is investigated on the basis of the approach of the theory of dynamic inversion. We consider the statement when the simultaneous reconstruction of disturbances in the deterministic and stochastic terms of the equation is performed with the use of discrete information on a number of realizations of a......
Stabilization of solution to the Cauchy problem for a parabolic equation with lower order coefficients and an exponentially growing initial function
Proceedings of the Steklov Institute of Mathematics - Tập 261 - Trang 94-97 - 2008
For the coefficients of lower order terms of a second-order parabolic equation, we obtain sharp sufficient conditions under which the solution of the Cauchy problem stabilizes to zero uniformly in x on each compact set K in ℝ
N
for any exponentially growing initial function.
Normal forms of families of maps in the Poincaré domain
Proceedings of the Steklov Institute of Mathematics - Tập 254 Số 1 - Trang 94-102 - 2006
Local controllability bifurcations in families of bidynamical systems on the plane
Proceedings of the Steklov Institute of Mathematics - Tập 261 - Trang 84-93 - 2008
We classify generic local controllability bifurcations in two-parameter families of bidynamical systems on the plane at points with nonzero velocity indicatrix.
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