Complete abstract differential equations of elliptic type with general Robin boundary conditions, in UMD spaces
type: Item
instance of: scholarly article
title: Complete abstract differential equations of elliptic type with general Robin boundary conditions, in UMD spaces
zbMATH Open document ID: 1242.34106
author: M. Cheggag
author: Angelo Favini
author: Rabah Labbas
author: Stéphane Maingot
author: A. Medeghri
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2011-03-22T00:00:00Z
review text: Let \(X\) be a UMD space. The authors consider the second order abstract differential equation \[ u''(x)+2Bu'(x)+Au(x)=f(x) \] for \( x\in (0,1)\), together with the abstract Robin boundary conditions: \[ u'(0)-Hu(0)=d_0; { } u(1)=u_1, \] where \(A\), \(B\) and \(H\) are linear operators on \(X\). Under various conditions on \(A\), \(B\) and \(H\), the authors prove the existence and uniqueness of the solution. As applications, two examples of partial differential equations are given to illustrate the results.
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5869365
zbMATH Keywords: abstract differential equations of second order
zbMATH Keywords: boundary value problem of Robin type
zbMATH Keywords: UMD spaces
MaRDI profile type: Publication
full work available at URL: dcdss.2011.4.523
OpenAlex ID: W2328078071
DOI: 10.3934/DCDSS.2011.4.523
description: scientific article; zbMATH DE number 5869365