Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Attractors For Parabolic Problems In Weighted Spaces, Xiaojun Li, Ying Tang
Attractors For Parabolic Problems In Weighted Spaces, Xiaojun Li, Ying Tang
Turkish Journal of Mathematics
The purpose of this paper is to investigate the asymptotic behavior of the solutions of parabolic equations with singular initial data in weighted spaces L^r_{\delta(x)}(\Omega) where \delta(x) is the distance to the boundary. We first establish the existence of the attractor for that equation in L^r_{\delta(x)}(\Omega) and then show the existence of the exponential attractor in L^2_{\delta(x)}(\Omega). In contrast to our previous results, we get the existence of attractors in weak topology spaces.