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Báo cáo hóa học: "Research Article Regularity of Parabolic Hemivariational Inequalities with Boundary Conditions"

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 Regularity of Parabolic Hemivariational Inequalities with Boundary Conditions | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 207873 22 pages doi 10.1155 2009 207873 Research Article Regularity of Parabolic Hemivariational Inequalities with Boundary Conditions Dong-Gun Park 1 Jin-Mun Jeong 2 and Sun Hye Park3 1 Mathematics and Materials Physics Dong-A University Saha-Gu Busan 604-714 South Korea 2 Division of Mathematical Sciences Pukyong National University Busan 608-737 South Korea 3 Department of Mathematics Pusan National University Busan 609-735 South Korea Correspondence should be addressed to Jin-Mun Jeong jmjeong@pknu.ac.kr Received 28 August 2008 Revised 4 December 2008 Accepted 1 January 2009 Recommended by Donal O Regan We prove the regularity for solutions of parabolic hemivariational inequalities of dynamic elasticity in the strong sense and investigate the continuity of the solution mapping from initial data and forcing term to trajectories. Copyright 2009 Dong-Gun Park 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 deal with the existence and a variational of constant formula for solutions of a parabolic hemivariational inequality of the form u x t ầ.u x t - div C e u x t E x t f x t in Q X 0 to 1.1 u x t 0 on r1 X 0 to 1.2 C e u x t v - v u x t on r0 X 0 to 1.3 E x t e y u x t a.e. x t Q X 0 to 1.4 u x 0 u0 x in Q 1.5 where Q is a bounded domain in RN with sufficiently smooth boundary r. Let x0 e RN p x x-x0 R maxxeQ x-x01. The boundary r is composed of two pieces r0 and r1 which 2 Journal of Inequalities and Applications are nonempty sets and defined by r0 x e r p x V a 0 r1 x e r P x V 0 1.6 where V is the unit outward normal vector to r. Here u du dt u u1 . uN T is the displacement e u 1 2 Vu Vu T 1 2 0ui 0Xj duị dXiỴ is the strain tensor y ù 1 u1 . pN uN T ựi is a .