CAJ | 학술논문

研究三维非线性Sobolev-Galpern方程Dirichlet初值问题的一个全离散有限差分格式.利用离散空间泛函分析和能量估计的方法证明了此数值格式的唯一可解性,同时得到了此差分格式的长时间的稳定性和收敛性.进一步,证明了离散动力系统整体吸引子的存在性以及离散动力系统的上半连续性.上述结果说明该数值离散格式可有效地模拟相应的无穷维动力系统.
연구삼유비선성Sobolev-Galpern방정Dirichlet초치문제적일개전리산유한차분격식.이용리산공간범함분석화능량고계적방법증명료차수치격식적유일가해성,동시득도료차차분격식적장시간적은정성화수렴성.진일보,증명료리산동력계통정체흡인자적존재성이급리산동력계통적상반련속성.상술결과설명해수치리산격식가유효지모의상응적무궁유동력계통.
A fully discrete difference scheme to the 3D nonlinear Sobolev-Galpern equation with Dirichlet initial-value problem is presented.The unique solvability of numerical solution is shown by using discrete space functional analysis and energy estimate method.The long-time stability and convergence of the scheme are proved.Furthermore,the existence of global attractor for the discrete dynamical system and the upper semicontinuity d(Ah,r,A)→0 are proved.Results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.