Cover Image

Behavior of the Double-Layer Potential for a Parabolic Equation on a Manifold

We prove that, similarly to the double-layer potential in \(\mathbb{R}^n \) , the double-layer potential constructed in a Riemann manifold of nonpositive sectional curvature has a jump in passing through the surface where its density is defined.

Saved in:

Bibliographic Details
Date:	2003
Main Authors:	Bernatskaya, J. N., Бернацька, Ю. Н.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 2003
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3935
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold
by: Bernatskaya, J. N., et al.
Published: (2008)

Perturbation Method for a Parabolic Equation with Drift on a Riemannian Manifold
by: Bernatskaya, J. N., et al.
Published: (2004)

Perturbed Parabolic Equation on a Riemannian Manifold
by: Bondarenko, V. G., et al.
Published: (2003)

Parametrix method for a parabolic equation on a Riemannian manifold
by: Bondarenko, V. G., et al.
Published: (1999)

Theorem on the central manifold of a nonlinear parabolic equation
by: Belan, E. P., et al.
Published: (1996)

Decay of the Solutions of Parabolic Equations with Double Nonlinearity and the Degenerate Absorption Potential
by: E. V. Stepanova
Published: (2014)

Decay of the Solutions of Parabolic Equations with Double Nonlinearity and the Degenerate Absorption Potential
by: Stepanova, E. V., et al.
Published: (2014)

Local sub-estimates of solutions to double phase parabolic equations via nonlinear parabolic potentials
by: K. O. Buryachenko
Published: (2019)

Local sub-estimates of solutions to double phase parabolic equations via nonlinear parabolic potentials
by: Buryachenko, K.O.
Published: (2019)

Central manifolds of quasilinear parabolic equations
by: Belan, E. P., et al.
Published: (1998)

Extinction of solutions of higher order parabolic equations with double nonlinearity and degenerate absorption potential
by: E. V. Stepanova
Published: (2014)

Quasilinear parabolic equations with a degenerate absorption potential
by: Ye. O. Yevhenieva
Published: (2018)

Parabolic Foliations on Three-Manifolds
by: Krouglov, V.
Published: (2009)

Behavior of blow-up solutions for quasilinear parabolic equations
by: Ye. O. Yevhenieva
Published: (2020)

Invariant manifolds for coupled nonlinear parabolic-hyperbolic partial differential equations
by: Fastovska, T.B.
Published: (2005)

Invariant manifolds for coupled nonlinear parabolic-hyperbolic partial differential equations
by: Fastovska, T. B., et al.
Published: (2005)

On Stabilization of Energy of a Conservative System Perturbed by a Random Process of “White-Noise” Type in the Itô Form
by: Bernatskaya, J. N., et al.
Published: (2001)

Limiting behavior of the solutions to linear second-order parabolic equations
by: Skrypnik, I. I., et al.
Published: (1993)

Integral manifolds and exponential splitting of linear parabolic equations with rapidly varying coefficients
by: Belan, E. P., et al.
Published: (1995)

Electromagnetic Wave Scattering by a Double-Periodic Magnetodielectric Layer
by: Sydorchuk, N. V., et al.
Published: (2013)

On a nonlocal problem for a parabolic equation
by: Berezansky, Yu. M., et al.
Published: (1995)

The Borsuk-Ulam Theorem for Double Coverings of Seifert Manifolds
by: A. Bauval, et al.
Published: (2013)

Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
by: McKay, B.
Published: (2011)

Asymptotic behavior of solutions for differential equations with double singularity in conditionally stable case
by: L. I. Karandzhulov
Published: (2018)

Asymptotic behavior of solutions for differential equations with double singularity in conditionally stable case
by: Karandzhulov, L.I.
Published: (2018)

On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes
by: Martynenko, A. V., et al.
Published: (2012)

Nonlocal Inverse Problem for a Parabolic Equation with Degeneration
by: Huzyk, N. M., et al.
Published: (2013)

Stefan problem for a weakly degenerate parabolic equation
by: Hryntsiv, N. M., et al.
Published: (2011)

On the Asymptotic Behavior of Solutions of the First Initial Boundary-Value Problems for Parabolic Equations
by: Nguyen Manh Hung, et al.
Published: (2003)

On the Asymptotic Behavior of Solutions of the First Initial Boundary-Value Problems for Parabolic Equations
by: Nguyen, Manh Hung, et al.
Published: (2003)

On behavior of solutions of the quasilinear second-order parabolic equations in unbounded noncylindrical domains
by: Kurta, V. V., et al.
Published: (1993)

Asymptotics of a parabolic problem with a nonsmooth angular function of the boundary layer
by: Omuraliev, Asan, et al.
Published: (2025)

Removability of an isolated singularity of solutions of the Neumann problem for quasilinear parabolic equations with absorption that admit double degeneration
by: Boldovskaya, O. M., et al.
Published: (2010)

On the problem of determining the parameter of a parabolic equation
by: Ashyralyev, A.
Published: (2010)

On the problem of determining the parameter of a parabolic equation
by: Ashyralyev, A., et al.
Published: (2010)

Nonlocal Inverse Problem for a Parabolic Equation with Degeneration
by: N. M. Huzyk
Published: (2013)

Modeling and determination of the unsteady thermoelastic state of a double-layer thermosensitive plate
by: Yu. Harmatii, et al.
Published: (2014)

Study of supercapacitors with a double electrical layer based on activated carbon materials
by: Budzulyak, I.M., et al.
Published: (2002)

Application of a recently proposed test to the hypernettedchain approximation for the electric double layer
by: Henderson, D., et al.
Published: (2007)

Ion size effects in a primitive level model of the diffuse double layer
by: Fawcett, W.R., et al.
Published: (2004)