| 一类三维拟抛物粘性扩散方程有限差分逼近的长时间行为 |
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| 引用本文： | 张磊,张巍岩.一类三维拟抛物粘性扩散方程有限差分逼近的长时间行为[J].工科数学,2012(4):31-38. |
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| 作者姓名： | 张磊 张巍岩 |
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| 作者单位： | [1]黑龙江大学数学科学学院,哈尔滨150080 [2]齐齐哈尔市恒昌中学,齐齐哈尔161005 |
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| 基金项目： | the Science Foundation of the Education Committee of Heilongjiang Province（12511416）; the Youth Foundation of Heilongjiang University（QL200804） |
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| 摘 要： | 研究了一类带有周期边界条件的三维拟抛物粘性扩散方程有限差分解的长时间行为.证明了数值解的存在唯一性,离散系统全局吸引子的存在性,差分格式的长时间稳定性和收敛性.此外,我们给出了上半连续性.
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| 关 键 词： | 拟抛物粘性扩散方程 Crank-Nikolson差分格式 全局吸引子 长时间误差估计 |
Long Time Behavior of Finite Difference Approximation for a Class of 3D Pseudo Parabolic Viscous Diffusion Equation |
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| ZHANG Lei,ZHANG Wei-yan.Long Time Behavior of Finite Difference Approximation for a Class of 3D Pseudo Parabolic Viscous Diffusion Equation[J].Journal of Mathematics For Technology,2012(4):31-38. |
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| Authors: | ZHANG Lei ZHANG Wei-yan |
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| Institution: | 1. Department of Mathematics, Heilongjiang University, Harbin 150080,China; 2. Qiqihar Hengchang Middle School, Qiqihar 161005, China) |
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| Abstract: | We studied the long-time behavior of the finite difference solution to a class of 3D pseudo parabolic viscous equation with periodic boundary conditions. The unique solvability of numerical solution, the existence of global attractor for the discrete system and the long time stability and convergence of the difference scheme are proved. Furthermore, the upper semicontinuity d（Ak,r,A） → 0 is given. |
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| Keywords: | pseudo parabolic viscous diffusion equation Crank-Nikolson difference scheme global attractor long time error estimate |
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