一般非线性演化方程的“暴力进程”及有关问题的讨论
The “Rebel Travelling” of General Nonlinear Evolutional Equation and Discussion on Related Problems
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摘要: 本文为系列讨论非线性演化方程“自身摧毁效应”的工作之一.文献[1,2]已讨论了流体力学的Navier-Stockes方程非线性演化的溃变.本文又进行了某些扩展,并涉及一、二阶模型的溃变和高阶复合型的“暴力进程”.结果表明,某些模型可在一定条件出现“半破裂”;溃变体现在整体演化中；对流体而言,弱非线性模型的人为性较强,且基于连续性思维的数值积分的平滑格式,及类似的作法或提法有待商榷.Abstract: This paper is a part of series works for diseussing the "auto-destruction effects" of general nonlinear evolutional equations.The blown-up of Navier-Stockes equation isdiscussed in references [1,2].Some expansion is made in this paper,and the blown-upof ordere-1 or 2 models and the "rebel travelling" of complex model of poly-order arediscussed.The results indicate that "semi-rupture" applears for some models on specific condition the blown-up appears during the whole evolution.For fluid however,the weadly-nonlinear model is of more artificiality and there is much room for arguing about the smoothing scheme of the numerical integral on the basis of continuous thinking and so on.
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Key words:
- “rebel travelling”,blown-up“semi-rupture” /
- whole evolution /
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[1] 欧阳首承等,《运动流体的"断裂"与天气预测的若干问题》, 成都科技大学出版社(1994),9-29.(in Chinese). [2] 欧阳首承, 泛系预测观与流体暴转, 应用数学和力学,16(3)(1995).269-277. [3] R.Thom,Stabilite Structurelle et Morphogenese.Reading.Moss: Benjamin(1972)(Structural Stability and Morphogenesis.W.A.Benjamin.Reading.Mass(1975).55-108. [4] A.Dauglas.Some existence theorems for hyperbolic systems of partial differentia l equation in two independent variables.Comm.Pure Appl.Math.2(1952).119-154. [5] 吴学谋,《从泛系观看世界》, 中国人民大学出版社(1990),21-28.(in Chinese). [6] 牟宗泽, 解奇异微分方程的一个新方法, 计算机应用(4)(1992) 20-27.(in Chinese). [7] E.N.Lorenz.Deterministric nonperiodic flow,J.Atmos.Sci.20(1963).130-141. [8] B.Saltzman.Finite amplitude free convection as initial value problem I.J.Atmos.Sci.19(1962),329-341. [9] 欧阳首承等, 关于Lorenz方程定常分叉解的联系问题, 成都气象学院学报,(2-3)(1990).112-114.(in Chinese) -
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