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Asymptotic behaviour of non-autonomous dissipative systems in Hilbert space

Part of: Differential equations in abstract spaces Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

Song Guozhu
Song Guozhu
Affiliation:
Department of Mathematics Nanjing UniversityNanjing 210008, China
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Abstract

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In this paper we discuss the asymptotic behaviour, as t → ∞, of the integral solution u(t) of the non-linear evolution equation where {A(t)}t≥0 is a family of m-dissipative operators in a Hilbert space H, and g ∈ Lloc (0, ∞ H).We give some sufficient conditions and some sufficient and necessary conditions to ensure that are weakly convergent.

Keywords

Non-linear evolution equationdissipative operatorintegral solutionasymptotic behaviour

MSC classification

Secondary: 47B44: Accretive operators, dissipative operators, etc. 34G20: Nonlinear equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 1 , February 1997 , pp. 93 - 103
Copyright
Copyright © Australian Mathematical Society 1997

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