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Báo cáo hóa học: " Research Article Existence of Global Attractors in Lp for m-Laplacian Parabolic Equation in RN"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence of Global Attractors in Lp for m-Laplacian Parabolic Equation in RN | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 563767 17 pages doi 10.1155 2009 563767 Research Article Existence of Global Attractors in Lp for m-Laplacian Parabolic Equation in RN Caisheng Chen 1 Lanfang Shi 1 2 and Hui Wang1 3 1 Department of Mathematics Hohai University Nanjing 210098 Jiangsu China 2 College of Mathematics and Physics Nanjing University of Information Science and Technology Nanjing 210044 Jiangsu China 3 Department of Mathematics Ili Normal University Yining 835000 Xinjiang China Correspondence should be addressed to Caisheng Chen cshengchen@hhu.edu.cn Received 4 April 2009 Revised 9 July 2009 Accepted 24 July 2009 Recommended by Zhitao Zhang We study the long-time behavior of solution for the m-Laplacian equation ut - div Vu m-2Vm x u m-2u f x ù g x in RN X R in which the nonlinear term f x u is a function like f x ù -h x u q-2u with h x 0 2 q m or f x u a x u a-2u - h x u p-2u with a x h x 0 and a p m. We prove the existence of a global L2 RN ư RN -attractor for any p m. Copyright 2009 Caisheng Chen et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In this paper we are interested in the existence of a global L2 RN LpfRN -attractor for the m-Laplacian equation ut - àmu A u m-2u f x ù g x x e RN t e R 1.1 with initial data condition u x 0 uo x x e Rn 1.2 where the m-Laplacian operator Amu div Vu m-2Vu 2 m N A 0. For the case m 2 the existence of global L2 RN L2 RN -attractor for 1.1 - 1.2 is proved by Wang in 1 under appropriate assumptions on f and g. Recently Khanmamedov 2 studied the existence of global L2 RN Lm RN -attractor for 1.1 - 1.2 with m mN N-m . Yang et al. in 3 investigated the global L2 RN Lp RN nW 1m RN -attractor 2 Boundary Value Problems Ap under the assumptions f x u u a1 u p - a2 u m - affx and fu x u affx with .