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Curved thin domains and parabolic equations

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Prizzi M., Rinaldi M., Rybakowski K.

Studia Mathematica

2002

tom 151

nr 2

109-140

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⁺.

Ograniczanie wyników

1 Studia Mathematica

1 Prizzi M.

1 Rinaldi M.

1 Rybakowski K.

1 2002

Wyniki wyszukiwania

Curved thin domains and parabolic equations