A. Shlapunov

activity

20192023

most citedMixed Problems with a Parameter

14 citations · 27 across the 15 of their papers we have counts for

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Showing 2022Show all

6 papers · 1 filter

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…

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