一般非线性演化方程的“暴力进程”及有关问题的讨论

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The “Rebel Travelling” of General Nonlinear Evolutional Equation and Discussion on Related Problems

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.
- “暴力进程” /
- 溃变 /
- “半破裂” /
- 整体演化
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.
- “rebel travelling”,blown-up“semi-rupture” /
- whole evolution /

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