Edge singular behavior for the heat equation on polyhedral cylinders in \(\mathbb R^3\)
type: Item
instance of: scholarly article
title: Edge singular behavior for the heat equation on polyhedral cylinders in \(\mathbb R^3\)
zbMATH Open document ID: 1263.35054
author: Jae Ryong Kweon
published in: Potential Analysis
publication date: 2013-02-15T00:00:00Z
review text: The heat equation in the polyhedral cylinder is considered. A priori estimates are obtained in not weighted Sobolev spaces. It is shown that the singular part of the solution is based on the representation of the corner singularity for the Poisson problem with zero Dirichlet boundary condition.
reviewed by: Ramzet M. Dzhafarov
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 6136717
zbMATH Keywords: edge singularity
zbMATH Keywords: regularity
zbMATH Keywords: stress intensity function
MaRDI profile type: Publication
full work available at URL: s11118-012-9288-7
OpenAlex ID: W2012152463
cites work: Q4073917
cites work: Q3729417
cites work: ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
cites work: The Fourier singular complement method for the Poisson problem. I: Prismatic domains
cites work: Sommes d'opérateurs linéaires et équations différentielles opérationnelles
cites work: Singular behavior of the solution of the periodic-Dirichlet heat equation in weighted \(L^p\)-Sobolev spaces
cites work: On the closedness of the sum of two closed operators
cites work: Équations différentielles abstraites
cites work: Q3682872
cites work: Q3470840
cites work: Edge Behavior of the Solution of an Elliptic Problem
cites work: Q4023365
cites work: Singular behavior of elliptic problems in non Hilbertian Sobolev spaces
cites work: Singularity functions at axisymmetric edges and their representation by Fourier series
cites work: The Fourier-Finite-Element Method for Poisson’s Equation in Axisymmetric Domains with Edges
cites work: Elliptic interface problems in axisymmetric domains. II: The Fourier-finite-element approximation of non-tensorial singularities
cites work: Asymptotics of solutions of the heat equation in cones and dihedra
cites work: An evolution compressible Stokes system in a polygon
cites work: Singularities of a compressible Stokes system in a domain with concave edge in \(\mathbb R^{3}\)
cites work: Q5628582
cites work: Singularities of the solution to the Dirichlet problem for a second-order equation in a neighborhood of an edge
cites work: Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods
DOI: 10.1007/S11118-012-9288-7
description: scientific article; zbMATH DE number 6136717