Institute of Applied Mathematics and Mechanics

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19962026

most citedLong-Time Asymptotics for the Camassa-Holm Equation

227 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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24 papers · 1 filter

math.AP2025★ 1 cited

Regularized Reconstruction of Scalar Parameters in Subdiffusion with Memory via a Nonlocal Observation

Andrii Hulianytskyi, Sergei Pereverzyev, Sergii Siryk +1

In the paper, we propose an analytical and numerical approach to identify scalar parameters (coefficients, orders of fractional derivatives) in the multi-term fractional differenti…

math.AP2022★ 1 cited

On a class of functional difference equations: explicit solutions, asymptotic behavior and applications

Nataliya Vasylyeva

For $ν \in [0, 1]$ and a complex parameter $σ,$ $R e σ > 0,$ we discuss a linear inhomogeneous functional difference equation with variable coefficients on a complex plane $z\in\mathbb…

math.AP2022★ 3 cited

Multi-term fractional linear equations modeling oxygen subdiffusion through capillaries

Vittorino Pata, Sergii Siryk, Nataliya Vasylyeva

For $0 < ν_{2} < ν_{1} \leq 1$ , we analyze a linear integro-differential equation on the space-time cylinder $Ω \times (0, T)$ in the unknown $u = u (x, t)$ $$\mathbf{D}_{t}^{ν_1}(\varrho_{1}u)-\m…

math.AP2021★ 7 cited

M-dissipative boundary conditions and boundary tuples for Maxwell operators

Matthias Eller, Illya M. Karabash

For Maxwell operators $(E, H) \to (i ε^{- 1} \nabla \times H, - i μ^{- 1} \nabla \times E)$ in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result…

math.AP2021

Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces

Sergey Degtyarev

We consider a Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces. The equation generalizes the heat equation to the case of fractional powe…

math.AP2021★ 23 cited

On the Local Behavior of Local Weak Solutions to some Singular Anisotropic Elliptic Equations

Simone Ciani, Igor I. Skrypnik, Vincenzo Vespri

We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations that involves both non-degenerate and singular operators. Throughout a para…

math.AP2018★ 11 cited

Generalization of the Keller-Osserman theorem for higher order differential inequalities

A. A. Kon'kov, A. E. Shishkov

We obtain exact conditions guaranteeing that any global weak solution of the differential inequality $$ \sum_{|α| = m} \partial^α a_α(x, u) \ge g (|u|) \quad \mbox{in } {\mathbb R}…

math.AP2018

Finite speed of propagation for the thin film equation in spherical geometry

Roman Taranets

We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative…

math.AP2018★ 7 cited

Localized peaking regimes for quasilinear parabolic equations

Andrey E. Shishkov, Yevgeniia A. Yevgenieva

This paper deals with the asymptotic behavior as $t \to T < \infty$ of all weak (energy) solutions of a class of equations with the following model representative: \begin{equa…

math.AP2017

On blow-up conditions for solutions of higher order differential inequalities

A. A. Kon'kov, A. E. Shishkov

For differential inequalities of the form $$ \sum_{|α| = m} (- 1)^m \partial^α a_α(x, u) \ge b (x) |u|^λ \quad \mbox{in } {\mathbb R}^n, \: n \ge 1, $$ where $a_{α}$ and $b$ are some…

math.AP2015

Classical solvability of the multidimensional free boundary problem for the thin film equation in the case of partial wetting

S. P. Degtyarev

We prove locally in time the existence of the unique smooth solution (including smooth interface) to the multidimensional free boundary problem for the thin film equation in the ca…

math.AP2014

On Fourier multipliers in function spaces with partial Hölder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions

S. P. Degtyarev

We give relatively simple sufficient conditions on a Fourier multiplier, so that it maps functions with the H $o ¨$ lder property with respect to a part of the variables to func…

math.AP2013★ 1 cited

The existence of a smooth interface in the evolutionary elliptic Muskat--Verigin problem with nonlinear source

Sergey P. Degtyarev

We study the two-phase Muskat--Verigin free-boundary problem for elliptic equations with nonlinear sources. The existence of a smooth solution and a smooth free boundary is proved…

math.AP2013★ 4 cited

Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations

S. P. Degtyarev

We prove locally in time the existence of a smooth solution for multidimensional two-phase Stefan problem for degenerate parabolic equations of the porous medium type. We establish…

math.AP2012

Mean value type inequalities for quasinearly subharmonic functions

Oleksiy Dovgoshey, Juhani Riihentaus

The mean value inequality is characteristic for upper semicontinuous functions to be subharmonic. Quasinearly subharmonic functions generalize subharmonic functions. We find the ne…

math.AP2012

Well-posedness of sudden directional diffusion equations

Piotr Bogusław Mucha, Piotr Rybka

Our goal is to establish existence with suitable initial data of solutions to general parabolic equation in one dimension, $u_{t} = L (u_{x})_{x}$ , where $L$ is merely a monotone function…

math.AP2011★ 1 cited

Propagation of Singularities of Nonlinear Heat Flow in Fissured Media

Andrey Shishkov, Laurent Veron

In this paper we investigate the propagation of singularities in a nonlinear parabolic equation with strong absorption when the absorption potential is strongly degenerate followin…

math.AP2010

Singular solutions to the heat equations with nonlinear absorption and Hardy potentials

Vitali Liskevich, Andrey Shishkov, Zeev Sobol

We study the existence and nonexistence of singular solutions to the equation $u_{t} - Δ u - \frac{κ}{∣ x ∣ ^{2}} u + ∣ x ∣^{α} u ∣ u ∣^{p - 1} = 0$ , $p > 1$ , in $R^{N} \times [0, \infty)$ , $N \geq 3$ , with a singul…

math.AP2010★ 2 cited

Potential estimates for quasi-linear parabolic equations

Vitali Liskevich, Igor I. Skrypnik, Zeev Sobol

For a class of divergence type quasi-linear degenerate parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via nonlinear Wol…

math.AP2010★ 7 cited

Gradient estimates for degenerate quasi-linear parabolic equations

Vitali Liskevich, Igor I. Skrypnik, Zeev Sobol

For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients form bounded with respect to the Lapla…

math.AP2008

Diffusion versus absorption in semilinear parabolic equations

Andrey Shishkov, Laurent Veron

We study the limit, when $k \to \infty$ , of the solutions $u = u_{k}$ of (E) $\prt_{t}u-Δu+ h(t)u^q=0$ in $\BBR^N\ti (0,\infty)$, $u_{k} (., 0) = k δ_{0}$ , with $q > 1$ , $h (t) > 0$ . If $h(t)=e^…

math.AP2008★ 16 cited

On the nature of ill-posedness of the forward-backward heat equation

Marina Chugunova, Illya M. Karabash, Sergei G. Pyatkov

We study the Cauchy problem with periodic initial data for the forward-backward heat equation defined by the J-self-adjoint linear operator L depending on a small parameter. The pr…

math.AP2007

Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

Andrey Shishkov, Laurent Veron

We study the limit behaviour of solutions of a class of solutions of nonlinear parabolic equations with a degenerate strong absorption. We prove that two types of phenomena can occ…

math.AP2006★ 6 cited

Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation

Vladimir P. Burskii, Alexei S. Zhedanov

We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that t…