THE FINITE DIFFERENCE METHOD FOR DISSIPATIVE KLEIN-GORDON-SCHRDINGER EQUATIONS IN THREE SPACE DIMENSIONS  

作　　者：Fayong Zhang Bo Han 

机构地区：[1]Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China School of Mathematical Science, Heilongjiang University, Harbin 150080, China [2]Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

出　　处：《Journal of Computational Mathematics》2010年第6期879-900,共22页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(No.10371077)

摘　　要：A fully discrete finite difference scheme for dissipative Klein-Gordon-SchrSdinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding the- orems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in H2 × H2 ×H1 over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.A fully discrete finite difference scheme for dissipative Klein-Gordon-SchrSdinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding the- orems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in H2 × H2 ×H1 over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

关 键 词：Dissipative Klein-Gordon SchrSdinger equations Finite difference method Error bounds Maximal attractor. 

分 类 号：O413.1[理学—理论物理] TS941.714[理学—物理]