journal6 ›› 2012, Vol. 33 ›› Issue (5): 19-22.DOI: 10.3969/j.issn.1007-2985.2012.05.005
• 数学 • 上一篇 下一篇
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基金资助:
国家自然科学基金资助项目（11101143）；中央高校基本科研业务费专项资金资助（10ML37，12MS83）
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摘要：研究1维零压流体运动方程组，引进势函数并讨论它的最小值点.当初值(x,t)∈R0,∞)时，得出解的局部结构的以下结论.若势函数有唯一非退化最小值点，则(x,t)附近的解光滑；若势函数有2个以上非退化最小值点或唯一退化最小值点，则(x,t)附近的解间断.
关键词： 零压流体运动方程组, 局部结构, 退化点, 非退化点
Abstract: This paper is concerned with one-dimensional zero-pressure flow equations.By introducing a potential function and discussing its minimizing point,the following conclusions on the local structure of the solution are drawn for each point (x,t)∈R×(0,∞).When potential function has a uniqe non-degenerate minimizing point,solutions are smooth in the neighborhood of (x,t);When potential function has more than two non-degenerate minimizing points or a uniqe degenerate minimizing point,solutions are discontinuous in the neighborhood of (x,t).
Key words: zero-pressure flow equations, local structure, degenerate point, non-degenerate point
张茜, 赵引川. 1维零压流体运动方程组的解的局部结构[J]. journal6, 2012, 33(5): 19-22.
ZHANG Qian, ZHAO Yin-Chuan. Local Structure of the Solutions to One-Dimensional Zero-Pressure Flow Equations[J]. journal6, 2012, 33(5): 19-22.
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链接本文: https://zkxb.jsu.edu.cn/CN/10.3969/j.issn.1007-2985.2012.05.005
https://zkxb.jsu.edu.cn/CN/Y2012/V33/I5/19
