Curved thin domains and parabolic equations

• Autorzy: M. Prizzi , M. Rinaldi , K. P. Rybakowski
• Języki publikacji: EN

Abstrakty

EN

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⁺.

Kategorie tematyczne

• 35K57: Reaction-diffusion equations
• 35P15: Estimation of eigenvalues, upper and lower bounds
• 53B21: Methods of Riemannian geometry
• 35B41: Attractors
• 35B25: Singular perturbations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 151
• Numer: 2
• Strony: 109-140

Daty

wydano

2002

Twórcy

autor

M. Prizzi

• Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Via Valerio, 12/b, 34100 Trieste, Italy

autor

M. Rinaldi

• DISCAFF, Viale Ferrucci, 33, 28100 Novara, Italy

autor

K. P. Rybakowski

• Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, 18055 Rostock, Germany

Identyfikatory

DOI

10.4064/sm151-2-2