Classical solutions of the first boundary value problem for parabolic systems on the plane

DOI10.1134/S1064562422020132zbMath1494.35092OpenAlexW4286652137MaRDI QIDQ2155334

A. N. Konenkov

Publication date: 15 July 2022

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562422020132

zbMATH Keywords

classical solutionone space dimensionfirst boundary value problemparabolic systemnonsmooth lateral boundary

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order parabolic systems (35K45) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Classical solutions to PDEs (35A09)

Related Items (3)

Existence and uniqueness of the classical solution of the first boundary value problem for parabolic systems on the plane ⋮ On the unique solvability of initial-boundary value problems for parabolic systems in bounded plane domains with nonsmooth lateral boundaries ⋮ Uniqueness of solutions to initial-boundary value problems for parabolic systems with dini-continuous coefficients in a semibounded domain on the plane

Cites Work

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• Simple layer potential and the first boundary value problem for a parabolic system on the plane
• Uniqueness of solutions of the first and second initial-boundary value problems for parabolic systems in bounded domains on the plane
• Uniqueness of the solution of the first initial-boundary value problem for a parabolic system with differentiable coefficients in a half-strip with nonsmooth lateral boundary
• Uniqueness of solutions to initial boundary value problems for parabolic systems in plane bounded domains with nonsmooth lateral boundaries
• ON THE MAXIMUM PRINCIPLE FOR STRONGLY ELLIPTIC AND PARABOLIC SECOND ORDER SYSTEMS WITH CONSTANT COEFFICIENTS
• Dirichlet problem for parabolic systems with Dini continuous coefficients
• Fundamental solutions of parabolic systems. I

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