Título :	Non-dissipative system as limit of a dissipative one : comparison of the asymptotic regimes
Autor :	Silva, Ricardo Parreira da
Assunto::	Sistemas dissipativos Sistemas não dissipativos Atratores globais Atratores não compactos Semicontinuidade superior Semicontinuidade inferior
Fecha de publicación :	2019
Editorial :	Springer
Citación :	SILVA, Ricardo Parreira da. Non-dissipative system as limit of a dissipative one: comparison of the asymptotic regimes. Bulletin of the Brazilian Mathematical Society, New Series v. 51, p.125-137, 2020. DOI: https://doi.org/10.1007/s00574-019-00146-z.
Abstract:	Let ⊂ Rn be a bounded smooth domain in Rn. Given u0 ∈ L2(), g ∈ L∞() and λ ∈ R, consider the family of problems parametrised by p 2, ⎧ ⎪⎨ ⎪⎩ ∂u ∂t − pu = λu + g, on (0,∞) × , u = 0, in (0,∞) × ∂, u(0, ·) = u0, on , where pu := div |∇u| p−2∇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.
DOI:	https://doi.org/10.1007/s00574-019-00146-z
metadata.dc.relation.publisherversion:	https://link.springer.com/article/10.1007/s00574-019-00146-z
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