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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 Asymptotic Stability of Solutions to Nonlinear Marine Riser Equation | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 504670 8 pages doi 10.1155 2010 504670 Research Article Global Asymptotic Stability of Solutions to Nonlinear Marine Riser Equation Sevket Gur Department of Mathematics Sakarya University 54100 Sakarya Turkey Correspondence should be addressed to Sevket Gur sgur@sakarya.edu.tr Received 28 May 2010 Revised 25 August 2010 Accepted 14 September 2010 Academic Editor Michel C. Chipot Copyright 2010 Sevket Gur. 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. This paper studies initial boundary value problem of fourth-order nonlinear marine riser equation. By using multiplier method it is proven that the zero solution of the problem is globally asymptotically stable. 1. Introduction The straight-line vertical position of marine risers has been investigated with respect to dynamic stability 1 . It studies the following initial boundary value problem describing the dynamics of marine riser mutt ElUxxxx - NeffUx x aUx but ut 0 x e 0 T t 0 1.1 u 0 t Uxx 0 t u l t Uxx l t 0 t 0 1.2 where EI is the flexural rigidity of the riser Neff is the effective tension a is the coefficient of the Coriolis force b is the coefficient of the nonlinear drag force and m is the mass line density. u represents the riser deflection. By using the Lyapunov function technique Kohl has shown that the zero solution of the problem is stable. In 2 Kalantarov and Kurt have studied the initial boundary value problem for the equation mutt kUxxxx - a x Ux x fUtx but ut p 0 1.3 2 Journal of Inequalities and Applications under boundary conditions 1.2 . Here p m k and b are given positive numbers Y is given real number a x is a C1 0 l function and a x -Co 0for all x e 0 . It is shown that the zero solution of the problem 1.3 - 1.2 is globally asymptotically
