Variational formulation and structural stability of monotone equations
type: Item
instance of: scholarly article
title: Variational formulation and structural stability of monotone equations
zbMATH Open document ID: 1304.47073
author: Augusto Visintin
published in: Calculus of Variations and Partial Differential Equations
publication date: 2013-05-07T00:00:00Z
review text: This very informative and well-written paper pertains to the author's ongoing research program which concerns the variational representation of nonlinear evolutionary partial differential equations and the application of variational methods to the analysis of the structural stability of such equations. It consists of three parts. The first one (Sections 1--3) provides an outline, as well as several pertinent examples, of the Fitzpatrick theory regarding monotone operators and their representative functions. The second part (Sections 4--6) is devoted to the \(\Gamma\)-convergence of representative functions. In the third part (Sections 7--9) of the paper, the author uses his previous results to study periodic (Section 7) and initial-value (Section 8) monotone flows. The possible onset of long memory in the limit is discussed in Section 9.
reviewed by: Simeon Reich
Mathematics Subject Classification ID: 47J22
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47J35
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 58E99
zbMATH DE Number: 6161252
zbMATH Keywords: gamma-convergence
zbMATH Keywords: long memory
zbMATH Keywords: monotone flow
zbMATH Keywords: monotone inclusion
zbMATH Keywords: monotone operator
zbMATH Keywords: representative function
zbMATH Keywords: structural stability
zbMATH Keywords: variational representation
MaRDI profile type: Publication
full work available at URL: s00526-012-0519-y
OpenAlex ID: W1973011532
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DOI: 10.1007/S00526-012-0519-Y

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