Approximation of evolution equations with polynomial reproducing nonlinearities
type: Item
instance of: scholarly article
title: Approximation of evolution equations with polynomial reproducing nonlinearities
zbMATH Open document ID: 0607.35051
DOI: 10.1007/BF00945084
author: M. Fiebig
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1986-01-01T00:00:00Z
review text: The author studies equations \(u'(t)=Au(t)+N(u(t))\) with polynomial nonlinearity N in a Banach space which lies in a Hilbert space. It is assumed that the nonlinear operator N is ''finitely reproducing'' relative to the orthonormal sequence generated by \(Au=\lambda u\). The major part of the paper deals with the problem \[ v_ t(x,t)=v_{xx}(x,t)+\sum^{3}_{j=0}a_ j(v(x,t))^ j,\quad t>0,\quad 0\leq x\leq \pi, \] \[ v_ x(0,t)=v_ x(\pi,t)=0,\quad t>0,\quad v(x,0)=\psi (x),\quad 0\leq x\leq \pi. \] The author proves the reproducing property of the nonlinear operator and gives numerical results on Faedo-Galerkin approximations.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 3981674
zbMATH Keywords: polynomial nonlinearity
zbMATH Keywords: finitely reproducing
zbMATH Keywords: Faedo-Galerkin approximations
reviewed by: Wolfgang Watzlawek
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00945084
OpenAlex ID: W2075923223
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description: scientific article; zbMATH DE number 3981674