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Consider the family
uₜ = Δu + G(u), t > 0, $x ∈ Ω_{ε}$,
$∂_{ν_{ε}}u = 0$, t > 0, $x ∈ ∂Ω_{ε}$, $(E_{ε})$
of semilinear Neumann boundary value problems, where, for ε > 0 small, the set $Ω_{ε}$ is a thin domain in $ℝ^{l}$, possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of $ℝ^{l}$. If G is dissipative, then equation $(E_{ε})$ has a global attractor $𝒜_{ε}$.
We identify a "limit" equation for the family $(E_{ε})$, prove convergence of trajectories and establish an upper semicontinuity result for the family $𝒜_{ε}$ as ε → 0⁺.
uₜ = Δu + G(u), t > 0, $x ∈ Ω_{ε}$,
$∂_{ν_{ε}}u = 0$, t > 0, $x ∈ ∂Ω_{ε}$, $(E_{ε})$
of semilinear Neumann boundary value problems, where, for ε > 0 small, the set $Ω_{ε}$ is a thin domain in $ℝ^{l}$, possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of $ℝ^{l}$. If G is dissipative, then equation $(E_{ε})$ has a global attractor $𝒜_{ε}$.
We identify a "limit" equation for the family $(E_{ε})$, prove convergence of trajectories and establish an upper semicontinuity result for the family $𝒜_{ε}$ as ε → 0⁺.
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Rocznik
Tom
Numer
Strony
109-140
Opis fizyczny
Daty
wydano
2002
Twórcy
autor
- Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Via Valerio, 12/b, 34100 Trieste, Italy
autor
- DISCAFF, Viale Ferrucci, 33, 28100 Novara, Italy
autor
- Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, 18055 Rostock, Germany
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-2-2