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báo cáo hóa học:" Research Article ¨ On Coupled Klein-Gordon-Schrodinger Equations with Acoustic 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: vResearch Article ¨ On Coupled Klein-Gordon-Schrodinger Equations with Acoustic Boundary Conditions | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 132751 23 pages doi 10.1155 2010 132751 Research Article On Coupled Klein-Gordon-Schrodinger Equations with Acoustic Boundary Conditions Tae Gab Ha1 and Jong Yeoul Park2 1 Department of Mathematics Iowa State University Ames IA 50011 USA 2 Department of Mathematics Pusan National University Busan 609-735 Republic of Korea Correspondence should be addressed to Tae Gab Ha tgha78@gmail.com Received 8 July 2010 Accepted 10 September 2010 Academic Editor Salim Messaoudi Copyright 2010 T. G. Ha and J. Y. 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. We are concerned with the existence and energy decay of solution to the initial boundary value problem for the coupled Klein-Gordon-Schrodinger equations with acoustic boundary conditions. 1. Introduction In this paper we are concerned with global existence and uniform decay for the energy of solutions of Klein-Gordon-Schrodinger equations iu1 Au i u 2u iau -uv in Q Q X 0 to v - Av f2v pv u 2 in Q Q X 0 to u 0 on S r X 0 to v 0 on So r0 X 0 to yv f x z g x z 0 on Si r1 X 0 to dv -A- h x z on S1 r1 X 0 to ov u x 0 u0 v x 0 v0 vfx 0 v1 in Q 1.1 where Q c R is a bounded domain 1 n 3 with boundary r r0 u r1 of class C2 where r0 and r1 are two disjoint pieces of r each having nonempty interior and f g h r1 R are 2 Boundary Value Problems given functions. We will denote by V the unit outward normal vector to r. A stands for the Laplacian with respect to the spatial variables denotes the derivative with respect to time t. Here z x t is the normal displacement to the boundary at time t with the boundary point x. The above equations describe a generalization of the classical model of the Yukawa interaction of conserved complex nucleon field with neutral real meson field. Here u is complex .