Coercive boundary value problems for parabolic overdetermined systems with variable coefficients
type: Item
instance of: scholarly article
title: Coercive boundary value problems for parabolic overdetermined systems with variable coefficients
zbMATH Open document ID: 0649.35066
DOI: 10.1007/BF01060774
author: M. A. Fel'dman
published in: Ukrainian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: One denotes by \((A,B)\) the boundary value problem operator \[ (A,B): {\mathcal E}(E_ 0')\to {\mathcal E}(E_ 1')\times {\mathcal E}(G_ 1') \] where \(B: y\to (B_ 1y)|_{\Gamma}\), and A and \(B_ 1\) are differential operators. If M is a smooth manifold with smooth boundary \(\Gamma\), \(\dim M=n\) and \(E_ i\), \(G_ i\) smooth finite dimensional vector fiberings on M respectively on \(\Gamma\), then \(E_ i'\) and \(G_ i'\) are their inverse images and \({\mathcal E}(E_ i')\), \({\mathcal E}(G_ i')\) are spaces of \(C^{\infty}\) smooth sections of fiberings \(E_ i'\) and \(G_ i'\). One denotes \(M'=M\times R^ 1\) and \(\Gamma '=\Gamma \times R^ 1\). For the operator (A,B) with the coefficients depending upon t, one builds an \(\partial-\gamma\) joint operator and one proves the solvability of the coercive boundary value problem, with the fulfillment of the compatibility condition on the finite and infinite interval in t.
Mathematics Subject Classification ID: 35N10
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4059972
zbMATH Keywords: smooth manifold
zbMATH Keywords: smooth boundary
zbMATH Keywords: finite dimensional vector fiberings
zbMATH Keywords: solvability
zbMATH Keywords: coercive boundary value problem
MaRDI profile type: Publication
cites work: Overdetermined parabolic boundary-value problems
cites work: Overdetermined systems of linear partial differential equations
cites work: Q5572526
cites work: ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
description: scientific article; zbMATH DE number 4059972