Weak solutions for nonlocal boundary value problems with low regularity data
type: Item
instance of: scholarly article
title: Weak solutions for nonlocal boundary value problems with low regularity data
zbMATH Open document ID: 1149.35052
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-05-15T00:00:00Z
review text: The author considers the following quasilinear parabolic initial boundary value problem \[ \begin{alignedat}{2}2 u_t+ A(t,x,u)u &= f(t, x,u) \quad&&\text{in }Q_T= (0,T)\times \Omega,\\ B(t,x,u)u &= k(t,x,u) \quad&&\text{on }\partial\Omega,\\ u(x,) &= u_0(x) \quad&&\text{in }\Omega, \end{alignedat} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^d\) \((d\geq 2)\), \(A(t,x,u)\) is strongly elliptic, and the boundary operator \(B\) is nonlocal. The goal of the author is to study weak (or very weak) solutions of the corresponding stationary and evolution problem related to the equations above. To this end the author uses maximal regularity.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 5152782
zbMATH Keywords: maximal regularity
author: Yuandi Wang
MaRDI profile type: Publication
full work available at URL: j.na.2006.05.002
OpenAlex ID: W2031803296
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DOI: 10.1016/J.NA.2006.05.002
description: scientific article; zbMATH DE number 5152782