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 ......
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......
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
On the Nikol’skii and Potapov classes of functions
Proceedings of the Steklov Institute of Mathematics - Tập 293 - Trang 216-227 - 2016
It is proved that the Nikol’skii classes H
1
r
and Potapov classes A
1
r
contain the class W
1
r
for......
Algebraic curve in the unit ball in ℂ2 that passes through the origin and all of whose boundary components are arbitrarily short
Proceedings of the Steklov Institute of Mathematics - Tập 253 Số 1 - Trang 123-143 - 2006
A negative answer is given to the following question of A.G. Vitushkin: Does there exist a nontrivial lower bound for the length of the maximal component of intersection of the unit sphere and an algebraic curve passing through the origin.
Integrability of Exceptional Hydrodynamic-Type Systems
Proceedings of the Steklov Institute of Mathematics - Tập 302 - Trang 325-335 - 2019
We consider non-diagonalizable hydrodynamic-type systems integrable by the extended hodograph method. We restrict the analysis to non-diagonalizable hydrodynamic reductions of the three-dimensionalMikhalev equation. We show that families of these hydrodynamictype systems are reducible to the heat hierarchy. Then we construct new particular explicit solutions for the Mikhalev equation.
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