Curved thin domains and parabolic equations
Tom 151 / 2002
Studia Mathematica 151 (2002), 109-140
MSC: Primary 35K57, 35B25, 35B41; Secondary 35P15, 53B21.
DOI: 10.4064/sm151-2-2
Streszczenie
Consider the family of semilinear Neumann boundary value problems, where, for \varepsilon>0 small, the set {\mit\Omega}_\varepsilon is a thin domain in \mathbb R^l, possibly with holes, which collapses, as \varepsilon\to0^+, onto a (curved) k-dimensional submanifold of \mathbb R^l. If G is dissipative, then equation (E_\varepsilon) has a global attractor {\mathcal A}_\varepsilon. We identify a “limit” equation for the family (E_\varepsilon), prove convergence of trajectories and establish an upper semicontinuity result for the family {\mathcal A}_\varepsilon as \varepsilon\to0^+.
