A. Shlapunov

activity

20192023

most citedMixed Problems with a Parameter

14 citations · 28 across the 19 of their papers we have counts for

collaborators

19 papers

math.AP2023★ 14 cited

Mixed Problems with a Parameter

Alexander Shlapunov, Nikolai Tarkhanov

Let $X$ be a smooth $n$ -dimensional manifold and $D$ be an open connected set in $X$ with smooth boundary $\partial D$ . Perturbing the Cauchy problem for an elliptic system $Au =…

math.AP2022★ 1 cited

On the ill-posed Cauchy problem for the polyharmonic heat equation

Ilya Kurilenko, Alexander Shlapunov

We consider the ill-posed Cauchy problem for the polyharmonic heat equation on recovering a function, satisfying the equation $(\partial_{t} + (- Δ)^{m}) u = 0$ in a cylindrical domain…

math.AP2022

Exterior extension problems for strongly elliptic operators: solvability and approximation using fundamental solutions

Vitaly Kalinin, Alexander Shlapunov

In this work we study three exterior extension problems for strongly elliptic partial equations: the Cauchy problem (in a special statement), the "analytical" continuation problem…

math.AP2022

Existence theorems for regular spatially periodic solutions to ersatz Navier-Stokes equations

Alexander Shlapunov

The initial problem for the Navier-Stokes type equations over $R^{n} \times [0, T]$ , $n \geq 2$ , with a positive time $T$ in the spatially periodic setting is considered. Fir…

math.AP2022

The Fredholm Navier-Stokes type equations for the de Rham complex over weighted Hölder spaces

Kseniya Gagelgans, Alexander Shlapunov

We consider a family of initial problems for the Navier-Stokes type equations generated by the de Rham complex in $R^{n} \times [0, T]$ , $n \geq 2$ , with a positive time $T$ …

math.AP2022

On approximation of solutions to the heat equation from Lebesgue class $L^{2}$ by more regular solutions

Alexander Shlapunov

Let $s \in N$ , $T_{1}, T_{2} \in R$ , $T_{1} < T_{2}$ , and $Ω, ω$ be bounded domains in $R^{n}$ , $n \geq 1$ , such that $ω \subset Ω$ and the complement $Ω\setminus ω…

math.AP2022

Approximation of solutions to parabolic Lamé type operators in cylinder domains and Carleman's formulas for them

Pavel Vilkov, Il'ya Kurilenko, Alexander Shlapunov

Let $s \in N$ , $T_{1}, T_{2} \in R$ , $T_{1} < T_{2}$ , and let $Ω, ω$ be bounded domains in $R^{n}$ , $n \geq 1$ such that $ω \subset Ω$ and the complement $Ω\setminu…

math.AP2021★ 5 cited

On uniqueness theorems for the inverse problem of Electrocardiography in the Sobolev spaces

Vitaly Kalinin, Alexander Shlapunov, Konstantin Ushenin

We consider a mathematical model related to reconstruction of cardiac electrical activity from ECG measurements on the body surface. An application of recent developments in solvin…

math.AP2021

Inverse image of precompact sets and existence theorems for the Navier-Stokes equations in spatially periodic setting

Alexander Shlapunov, Nikolai Tarkhanov

We consider the initial problem for the Navier-Stokes equations over $R^{3} \times [0, T]$ with a positive time $T$ in the spatially periodic setting. Identifying periodic v…

math.AP2021

On the uniqueness theorems for transmissions problems related to models of elasticity, diffusion and electrocardiography

Alexander Shlapunov, Yulia Shefer

We consider a generalization of the inverse problem of the electrocardiography in the framework of the theory of elliptic and parabolic differential operators. More precisely, star…

math.AP2020

Existence theorems for regular solutions to the Cauchy problem for the Navier-Stokes equations in $R^{3}$

Alexander Shlapunov, Nikolai Tarkhanov

We consider the initial problem for the Navier-Stokes equations over $R^{3} \times [0, T]$ with a positive time $T$ over specially constructed scale of function spaces of Bo…

math.AP2020★ 1 cited

Existence Theorems for Regular Spatially Periodic Solutions to the Navier-Stokes Equations

Alexander Shlapunov, Nikolai Tarkhanov

We consider the initial value problem for the Navier-Stokes equations over $R^{3} \times [0, T]$ with a positive time $T$ in the spatially periodic setting. Identifying periodic vec…

math.AP2020

On the stability phenomenon of the Navier-Stokes type Equations for Elliptic Complexes

Andrei Parfenov, Alexander Shlapunov

Let $X$ be a Riemannian $n$ -dimensional smooth compact closed manifold, $n \geq 2$ , $E^{i}$ be smooth vector bundles over $X$ and ${A^{i}, E^{i}}$ be an elliptic diff…

math.AP2019

On a Singular Perturbation of the Navier-Stokes Equations

Alexander Shlapunov, Nikolai Tarkhanov

The paper is aimed at analysing a singular perturbation of the Navier-Stokes equations on a compact closed manifold. The case of compact smooth manifolds with boundary under the Di…

math.AP2019

On the completeness of the root functions of the Sturm-Liouville problems for the Lamé system in weighted spaces

A. Peicheva. A. Shlapunov

We consider three Sturm--Liouville boundary value problems (the coercive ones and the non-coercive one) in a bounded Lipschitz domain for the perturbed Lamé operator with the bound…

math.AP2019★ 1 cited

An Open Mapping Theorem for the Navier-Stokes Equations

A. Shlapunov, N. Tarkhanov

We consider the Navier-Stokes equations in the layer $R^{n} \times [0, T]$ over $R^{n}$ with finite $T > 0$ . Using the standard fundamental solutions of the Laplace o…

math.AP2019★ 4 cited

On a mixed problem for the parabolic Lam'e type operator

R. Puzyrev, A. Shlapunov

We consider a boundary value problem for the parabolic Lamé type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consis…

math.AP2019

On Completeness of Root Functions of Sturm-Liouville Problems with Discontinuous Boundary Operators

A. Shlapunov, N. Tarkhanov

We consider a Sturm--Liouville boundary value problem in a boun\-ded domain $\cD$ of $R^{n}$ . By this is meant that the differential equation is given by a second order elli…

math.AP2019★ 2 cited

On non-coercive mixed problems for parameter-dependent elliptic operators

A. Polkovnikov, A. Shlapunov

We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain $D$ of $R^{n}$ for a second order parameter-dependent elliptic differential operato…

Mixed Problems with a Parameter

On the ill-posed Cauchy problem for the polyharmonic heat equation

Exterior extension problems for strongly elliptic operators: solvability and approximation using fundamental solutions

Existence theorems for regular spatially periodic solutions to ersatz Navier-Stokes equations

The Fredholm Navier-Stokes type equations for the de Rham complex over weighted Hölder spaces

On approximation of solutions to the heat equation from Lebesgue class L2 by more regular solutions

Approximation of solutions to parabolic Lamé type operators in cylinder domains and Carleman's formulas for them

On uniqueness theorems for the inverse problem of Electrocardiography in the Sobolev spaces

Inverse image of precompact sets and existence theorems for the Navier-Stokes equations in spatially periodic setting

On the uniqueness theorems for transmissions problems related to models of elasticity, diffusion and electrocardiography

Existence theorems for regular solutions to the Cauchy problem for the Navier-Stokes equations in R3

Existence Theorems for Regular Spatially Periodic Solutions to the Navier-Stokes Equations

On the stability phenomenon of the Navier-Stokes type Equations for Elliptic Complexes

On a Singular Perturbation of the Navier-Stokes Equations

On the completeness of the root functions of the Sturm-Liouville problems for the Lamé system in weighted spaces

An Open Mapping Theorem for the Navier-Stokes Equations

On a mixed problem for the parabolic Lam'e type operator

On Completeness of Root Functions of Sturm-Liouville Problems with Discontinuous Boundary Operators

On non-coercive mixed problems for parameter-dependent elliptic operators

On approximation of solutions to the heat equation from Lebesgue class $L^{2}$ by more regular solutions

Existence theorems for regular solutions to the Cauchy problem for the Navier-Stokes equations in $R^{3}$