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 and Asymptotic Stability of Solutions for Hyperbolic Differential Inclusions with a Source Term | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 56350 13 pages doi 2007 56350 Research Article Existence and Asymptotic Stability of Solutions for Hyperbolic Differential Inclusions with a Source Term Jong Yeoul Park and Sun Hye Park Received 10 October 2006 Revised 26 December 2006 Accepted 16 January 2007 Recommended by Michel Chipot We study the existence of global weak solutions for a hyperbolic differential inclusion with a source term and then investigate the asymptotic stability of the solutions by using Nakao lemma. Copyright 2007 J. Y. Park and S. H. Park. 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 concerned with the global existence and the asymptotic stability of weak solutions for a hyperbolic differential inclusion with nonlinear damping and source terms y 0 ytt - kyt - div Vy p-2Vy s A y m-2y in o X 0 00 s x t G p yt x t . x t G o X 0 00 on do X 0 00 y x 0 ye x yt x 0 y1 x in x G o where o is a bounded domain in RN with sufficiently smooth boundary do p 2 A 0 and p is a discontinuous and nonlinear set-valued mapping by filling in jumps of a locally bounded function b. Recently a class of differential inclusion problems is studied by many authors 2 6 7 11 14-16 19 . Most of them considered the existence of weak solutions for differential inclusions of various forms. Miettinen 6 Miettinen and Panagiotopoulos 7 proved the existence of weak solutions for some parabolic differential inclusions. J. Y. Park et al. 14 showed the existence of a global weak solution to the hyperbolic differential inclusion 2 Journal of Inequalities and Applications with A 0 by making use of the Faedo-Galerkin approximation and then considered asymptotic stability of the solution by using Nakao lemma 8 . The .
