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A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

✍ Scribed by Tomás Caraballo; Alexandre N. Carvalho; José A. Langa; Felipe Rivero

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 300 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.11.032

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✦ Synopsis

In this paper we consider the strongly damped wave equation with time-dependent terms

in a bounded domain Ω ⊂ R n , under some restrictions on β ε (t), γ (t) and growth restrictions on the nonlinear term f . The function β ε (t) depends on a parameter ε, β ε (t) ε→0 -→ 0.

We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A ε (t) : t ∈ R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at ϵ = 0.

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