| 带有多项式非线性项的高维反应扩散方程有限差分格式的长时间行为 |
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| 引用本文： | 王珏,张法勇.带有多项式非线性项的高维反应扩散方程有限差分格式的长时间行为[J].计算数学,2007,29(2):177-188. |
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| 作者姓名： | 王珏 张法勇 |
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| 作者单位： | 1. 哈尔滨工程大学理学院,哈尔滨,150001
2. 黑龙江大学数学科学学院,哈尔滨,150080 |
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| 基金项目： | 国家自然科学基金(No．10371077)资助项目． |
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| 摘 要： | 本文考虑了一类带有多项式非线性项的高维反应扩散方程．建立了一个全离散的有限差分格式,并证明了差分解的存在唯一性．分析了由差分格式生成的离散系统的动力性质,在对差分解先验估计的基础上得到了离散动力系统的整体吸引子的存在性．最后证明了差分格式的长时间稳定性和收敛性．
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| 关 键 词： | 整体吸引子 反应扩散方程 有限差分法 稳定性 收敛性 |
| 修稿时间： | 2006-01-14 |
LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SCHEME TO HIGHER-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH A POLYNOMIAL NONLINEARITY |
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| Wang Jue,Zhang Fayong.LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SCHEME TO HIGHER-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH A POLYNOMIAL NONLINEARITY[J].Mathematica Numerica Sinica,2007,29(2):177-188. |
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| Authors: | Wang Jue Zhang Fayong |
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| Institution: | 1.School of Science, Harbin Engineering University, Harbin 150001, China;2.Department of Mathematics, HeiLongJiang University, Harbin 150080, China |
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| Abstract: | In this paper, a class of higher-dimensional reaction-diffusion equations with a polynomial nonlinearity is considered. A fully discrete finite difference scheme is established. The existence and uniqueness of the difference solutions are achieved, and then the dynamical behaviour of the discrete system is analysed. The existence of global attractor of the discrete system are proved by a priori estimate of the difference solution. Finally, long-time stability and convergence of the difference scheme are proved. |
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| Keywords: | Global attrator Reaction-diffusion equation Finite difference method Stability and Convergence |
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