Asymptotics of solutions of the heat equation in cones and dihedra

DOI10.1002/mana.201100192zbMath1258.35110OpenAlexW1966287718MaRDI QIDQ2909658

Jürgen Rossmann, Vladimir A. Kozlov

Publication date: 6 September 2012

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201100192

zbMATH Keywords

edgesweighted Sobolev spacesconical points

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) Asymptotic expansions of solutions to PDEs (35C20) Green's functions for elliptic equations (35J08)

Related Items (7)

On the nonstationary Stokes system in a cone ⋮ Edge singular behavior for the heat equation on polyhedral cylinders in \(\mathbb R^3\) ⋮ On the Neumann problem for the nonstationary Stokes system in angles and cones ⋮ On the behavior of solutions of the nonstationary Stokes system near the vertex of a cone ⋮ On the nonstationary Stokes system in a cone \((L_p\) theory) ⋮ Asymptotics of solutions of second order parabolic equations near conical points and edges ⋮ On the nonstationary Stokes system in a cone: asymptotics of solutions at infinity

Cites Work

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• Singular behavior of the solution of the periodic-Dirichlet heat equation in weighted \(L^p\)-Sobolev spaces
• On asymptotics of the Green function and Poisson kernels of a mixed parabolic problem in a cone. I
• Coefficients in the asymptotic solutions of the Cauchy boundary-value parabolic problems in domains with a conical point
• Solvability of the classical initial-boundary-value problems for the heat-conduction equation in a dihedral angle
• On asymptotics of the Green function and Poisson kernels of a mixed parabolic problem in a cone. II
• The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients
• Coefficients of the singularities of elliptic and parabolic problems in domains with edges

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