TY - JOUR
AU - Elsken, Thomas
AU - Prizzi, Martino
PY - 2002/09/01
Y2 - 2022/01/17
TI - Characterization of the limit of some higher dimensional thin domain problems
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 20
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2002.031
SP - 151 - 178
AB - A reaction-diffusion equation on a family of three dimensional thindomains, collapsing onto a two dimensional subspace, is considered.In [< i> The effect of domain squeezing upon the dynamicsof reaction-diffusion equations< /i> , J. Differential Equations < b> 173< /b> (2001), 271–320] it was proved that, as the thickness of the domainstends to zero, thesolutions of the equations converge in a strong sense to the solutions ofan abstract semilinear parabolic equation living in a closed subspace of$H^1$. Also, existence and upper semicontinuity of the attractors wasproved. In this work, for a specific class of domains, the limit problemis completely characterized as a system of two-dimensionalreaction-diffusion equations, coupled by mean of compatibility and balanceboundary conditions.
ER -