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Asymptotic behaviour of non-autonomous dissipative systems in Hilbert space
- Part of
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 62 / Issue 1 / February 1997
- Published online by Cambridge University Press:
- 09 April 2009, pp. 93-103
- Print publication:
- February 1997
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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.
where {
are weakly convergent.