Convergence of solutions of implicit differential equations
type: Item
instance of: scholarly article
title: Convergence of solutions of implicit differential equations
zbMATH Open document ID: 0802.34072
author: Angelo Favini
author: Viorel Barbu
published in: Differential and Integral Equations
publication date: 1994-06-29T00:00:00Z
review text: The convergence of solutions of the implicit differential equations (1) \(d(B_ n y)(t)/dt+ (A_ n y)(t)= f_ n(t)\), \((B_ n y)(0)= z^ n_ 0\), \(t\in [0,T]\), is studied. Here \(\{A_ n\}\), \(\{B_ n\}\) are two families of operators in a Banach space convergent in the sense of graph to operators \(A\) and \(B\), respectively. Both the case of nonlinear subpotential operators \(A_ n\), \(B_ n\) and linear ones is investigated. The techniques used in considerations are highly nontrivial and involve such tools as maximal monotone operators, subdifferentials, semigroups of operators and Sobolev spaces, for example. Applications of the results obtained to nonlinear degenerate parabolic equations, to optimal control theory and to the theory of linear operators are discussed.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35L80
zbMATH DE Number: 597483
zbMATH Keywords: convergence of solutions
zbMATH Keywords: implicit differential equations
zbMATH Keywords: Banach space
zbMATH Keywords: nonlinear degenerate parabolic equations
zbMATH Keywords: optimal control theory
zbMATH Keywords: theory of linear operators
reviewed by: Józef Banaś
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 597483