| 具耗散一维可压流体方程组奇性形成(英文) |
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| 引用本文： | 刘法贵,秦玉明.具耗散一维可压流体方程组奇性形成(英文)[J].郑州大学学报(理学版),2002,34(3):1-7. |
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| 作者姓名： | 刘法贵 秦玉明 |
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| 作者单位： | 1. 华北水利水电学院,郑州,450008
2. 河南大学数学系,河南,开封,475001 |
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| 基金项目： | 河南省高校杰出科研创新人才工程项目，河南省高校青年骨干教师资助项目 |
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| 摘 要： | 考虑具耗散项2αu（α＞0）可压缩流体方程组Cauchy问题经典解整体存在性与解的奇性形成，如果熵和α小于声波能量，证明了其经典解必在有限时间内产生激波， 进一步给出了经典解的生命区间跨度估计。
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| 关 键 词： | 可压流体方程组 奇性 耗散 Cauchy问题 经典解 整体存在性 生命区间跨度估计 |
Formation of Singularities in One-dimensional Compressible Fluids with Dissipative Term |
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| Abstract.Formation of Singularities in One-dimensional Compressible Fluids with Dissipative Term[J].Journal of Zhengzhou University:Natural Science Edition,2002,34(3):1-7. |
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| Authors: | Abstract |
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| Abstract: | The global existence and formation of singularities of classical solutions to the Cauchy problem in one-dimensionalcompressible fluids with dissipative term 2au(α>0) are considered. It is proved that if the initial amount of the entropy and a are smaller than that of sound waves, then classical (periodic) solutions will develop shocks in a finite time. Moreover, some quantitative estimates of lifespan of classical (periodic) solutions and a result on global existence of classical solutions are given. |
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| Keywords: | singularity compressible fluids dissipation Cauchy problem |
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