On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type
type: Item
instance of: scholarly article
title: On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type
zbMATH Open document ID: 0802.65113
author: I. Hlaváček
author: Michal Křížek
author: Jan Malý
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-08-17T00:00:00Z
review text: This paper deals with a quasilinear problem whose classical formulation reads: Find \(u\in C^ 1(\overline\Omega)\) such that \(u\bigl|_ \Omega\in C^ 2(\Omega)\) and \(-\text{div}(A(x,u)\text{grad }u)+ c(x,u)u= f(x,u)\) in \(\Omega\), \(u= \bar u\) on \(\Gamma_ 1\), \(n^ T A(s,u)\text{grad }u+ \alpha(s,u) u= g(s,u)\) on \(\Gamma_ 2\). Precise assumption upon the functions are given. The existence and uniqueness of weak and Galerkin solutions are investigated. A heat conduction problem which describes a temperature distribution in large transformers is presented.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 617450
zbMATH Keywords: quasilinear nonpotential elliptic problem
zbMATH Keywords: nonmonotone type
zbMATH Keywords: Galerkin method
zbMATH Keywords: heat conduction problem
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1192
OpenAlex ID: W2063614254
DOI: 10.1006/JMAA.1994.1192
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description: scientific article; zbMATH DE number 617450