tailieunhanh - Báo cáo hóa học: "PARABOLIC INEQUALITIES WITH NONSTANDARD GROWTHS AND L1 DAT"

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: PARABOLIC INEQUALITIES WITH NONSTANDARD GROWTHS AND L1 DAT | PARABOLIC INEQUALITIES WITH NONSTANDARD GROWTHS AND L1 DATA R. ABOULAICH B. ACHCHAB D. MESKINE AND A. SOUISSI Received 25 July 2005 Revised 13 December 2005 Accepted 19 December 2005 We prove an existence result for solutions of nonlinear parabolic inequalities with L1 data in Orlicz spaces. Copyright 2006 R. Aboulaich 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 Let D be an open bounded subset of RN N 2 let Q be the cylinder D X 0 T with some given T 0. Consider the following nonlinear parabolic problem du dt A u X in Q u x t 0 on dD X 0 T u x 0 u0 in D where A u -div a x t u u is a Leray-Lions operator defined on D A c W0 xLM D with M is an N-function and X is a given data. In the variational case . where X w-1 xEm D it is well known that the solvability of is done by Donaldson 2 and Robert 11 when the operator A is monotone t2 M t and M satisfies a A2 condition and by finally the recent work 3 for the general case. In the L1 case an existence theorem is given in 4 . However the techniques used in 4 do not allow us to adapt it for parabolic inequalities. It is our purpose in this paper to solve the obstacle problem associated to in the case where X L1 Q w-1 xEm Q and without assuming any growth restriction on M. The existence of solutions is proved via a sequence of penalized problems with solutions un. A priori estimates of the truncation of un are obtained in some suitable Orlicz space. For the passage to the limit the Hindawi Publishing Corporation Boundary Value Problems Volume 2006 Article ID 29286 Pages 1-18 DOI BVP 2006 29286 2 Parabolic inequalities in L1 almost everywhere convergence of V un is proved via new techniques. As operators models we can consider slow or fast growth A u --div 1 u 2Vulog 1 Vul t Vu A u - div Vu exp Vu . For some .