A monotone iterative scheme for nonlinear reaction-diffusion systems having nonmonotone reaction terms
type: Item
instance of: scholarly article
title: A monotone iterative scheme for nonlinear reaction-diffusion systems having nonmonotone reaction terms
zbMATH Open document ID: 0661.65126
DOI: 10.1016/0022-247X(88)90008-X
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: In der vorliegenden Arbeit wird ein monotones Iterationsschema vorgestellt zur näherungsweisen Lösung eines halblinearen Systems von Diffusionsgleichungen. Die Nichtlinearität tritt dabei als schwache Kopplung in den Reaktionstermen auf. Bemerkenswert ist an dem Verfahren, daß im Gegensatz zu früher konstruierten Verfahren keine Monotonie- Forderungen an die nichtlinearen Reaktionsterme gestellt werden müssen. Die Funktionenfolgen werden als Lösungen gewisser linearer Ersatzprobleme konstruiert und schließen die Lösung des ursprünglichen Anfangs-Randwertproblems von oben und unten ein. In konkreten Fällen allerdings kann das Auffinden geeigneter Startlösungen Schwierigkeiten bereiten. Da der Lösungsbegriff hier im schwachen Sinne formuliert ist, kommt man mit relativ schwachen Glattheitsbedingungen an die Daten des Problems aus.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 4080848
zbMATH Keywords: monotone iterative scheme
zbMATH Keywords: nonlinear
zbMATH Keywords: weakly coupled systems of reaction- diffusion equations
zbMATH Keywords: weak solutions
author: S. Carl
reviewed by: K.Finck von Finckenstein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4080848