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Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Parabolic problems with data measure Mohammmed Kbiri Alaoui | Alaoui Boundary Value Problems 2011 2011 46 http www.boundaryvalueproblems.eom content 2011 1 46 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Parabolic problems with data measure Mohammmed Kbiri Alaoui Correspondence mka_la@yahoo.fr Department of Mathematics King Khalid University P.O. Box 9004 Abha Kingdom of Saudi Arabia Abstract The article deals with the existence of solutions of some unilateral problems in the Orlicz-Sobolev spaces framework when the right-hand side is a Radon measure. Mathematics Subject Classification 35K86. Keywords unilateral problem radon measure Orlicz-Sobolev spaces 1 Introduction We deal with boundary value problems u Ỷ a.e. in Q X 0 T 9 u A u X in Q d t _ u 0 on dQ dfà X 0 T u x 0 u0 x in P where A u div a . t u Vu T 0 and o is a bounded domain of RN with the segment property. a o X R X RN RN is a Carathéodory function that is measurable with respect to x in o for every t s f in R X R X RN and continuous with respect to s f in R X RN for almost every x in o such that for all f f e RN f f a x t s ệ ệ aM ệ 1.1 a x t s ệ a x t s ệ p ệ 0 1.2 a x t s c x t k1P 1M k2 s k3M 1M k41 1-3 where c x t belongs to Em Q c 0 P is an N-function such that P M and ki i 1 2 3 4 belongs to R and a to R . X e M Q u0 e M a 1.4 Ỷ e L n W EV Lì . 1.5 There have obviously been many previous studies on nonlinear differential equations with nonsmooth coefficients and measures as data. The special case was cited in the references see 1 2 . Springer 2011 Alaoui licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Alaoui Boundary Value Problems 2011 2011 46 http www.boundaryvalueproblems.eom content 2011 1 46 Page 2 of 15 It is noteworthy that the articles mentioned above differ in significant way in the terms of
