Journal
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
Volume 51, Issue 1, Pages 125-137Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00574-019-00146-z
Keywords
Dissipative systems; Non-dissipative systems; Global attractors; Non-compact attractors; Upper-semicontinuity; Lower-semicontinuity
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Funding
- FAPDF [193.001.372/2016]
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Let Omega subset of R-n be a bounded smooth domain in R-n. Given u(0) is an element of L-2(Omega), g is an element of L-infinity (Omega) and lambda is an element of R, consider the family of problems parametrised by p SE arrow 2, {partial derivative u/partial derivative t - Delta(p)u = lambda u + g, on (0, infinity) x Omega, u = 0, in (0, infinity) x partial derivative Omega, u(0, center dot) = u(0), on Omega, where Delta(p)u := div(vertical bar del u vertical bar(p-2)del u) denotes the p-laplacian operator. Our aim in this paper is to describe the asymptotic behavior of this family of problems comparing compact attractors in the dissipative case p > 2, with non-compact attractors in the non-dissipative limiting case p = 2 with respect to the Hausdorff semi-distance between then.
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