tailieunhanh - báo cáo hóa học:" Research Article Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation"

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 Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 895121 10 pages doi 2010 895121 Research Article Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation Yaojun Ye Department of Mathematics and Information Science Zhejiang University of Science and Technology Hangzhou 310023 China Correspondence should be addressed to Yaojun Ye yeyaojun2002@ Received 14 December 2009 Accepted 18 March 2010 Academic Editor Shusen Ding Copyright 2010 Yaojun Ye. 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. The initial boundary value problem for a class of hyperbolic equation with nonlinear dissipative term uff - n 1 d ồxi du dxi P-2 du ồxiỴ a uf q-2uf b u r-2u in abounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set in Wtf Q and show the asymptotic behavior of the global solutions through the use of an important lemma of Komornik. 1. Introduction We are concerned with the global solvability and asymptotic stability for the following hyperbolic equation in a bounded domain n utt - fdxi i 1 i du dxi p 2 du dxi a ut q 2ut b u r 2u x e Q t 0 with initial conditions u x 0 u0 x ut x 0 u1 x x e Q and boundary condition u x t 0 x e dQ t 0 2 Journal of Inequalities and Applications where Q is a bounded domain in Rn with a smooth boundary dQ a b 0 and q r 2 are real numbers and Ap - n 1 d dXi d dXi p-2 d dx is a divergence operator degenerate Laplace operator with p 2 which is called a p-Laplace operator. Equations of type are used to describe longitudinal motion in viscoelasticity mechanics and can also be seen as field equations governing the longitudinal motion of a viscoelastic configuration obeying the nonlinear Voight model 1-4 . For b 0 it is .