@article{Elsken_Prizzi_2002, title={Characterization of the limit of some higher dimensional thin domain problems}, volume={20}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2002.031}, abstractNote={A reaction-diffusion equation on a family of three dimensional thin
domains, collapsing onto a two dimensional subspace, is considered.
In [< i> The effect of domain squeezing upon the dynamics
of reaction-diffusion equations< /i> , J. Differential Equations < b> 173< /b> (2001), 271–320] it was proved that, as the thickness of the domains
tends to zero, the
solutions of the equations converge in a strong sense to the solutions of
an abstract semilinear parabolic equation living in a closed subspace of
$H^1$. Also, existence and upper semicontinuity of the attractors was
proved. In this work, for a specific class of domains, the limit problem
is completely characterized as a system of two-dimensional
reaction-diffusion equations, coupled by mean of compatibility and balance
boundary conditions.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Elsken, Thomas and Prizzi, Martino}, year={2002}, month={Sep.}, pages={151–178} }