| 一类高维拟线性对角型双曲组经典解的生命区间及其应用 |
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| 引用本文： | 孔德兴.一类高维拟线性对角型双曲组经典解的生命区间及其应用[J].复旦学报(自然科学版),1992(4). |
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| 作者姓名： | 孔德兴 |
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| 作者单位： | 复旦大学数学研究所 1991级博士研究生 |
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| 摘 要： | 在非常一般的条件下,对一类高维拟线性对角型双曲组,考察了具有紧支集初值的Cauchy问题,证明了其经典解必在有限时刻破裂(blow—up);特别地,对紧支集小初值的情况,给出了经典解的生命区间及其在非线性波动方程中的应用.
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| 关 键 词： | 拟线性 波动方程 破裂 生命区间 |
LIFE-SPAN OF CLASSICAL SOLUTIONS OF QUASIUNEAR HYPERBOLIC SYSTEMS IN HIGH DIMENSIONS AND ITS APPLICATIONS |
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| Kong Dexing.LIFE-SPAN OF CLASSICAL SOLUTIONS OF QUASIUNEAR HYPERBOLIC SYSTEMS IN HIGH DIMENSIONS AND ITS APPLICATIONS[J].Journal of Fudan University(Natural Science),1992(4). |
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| Authors: | Kong Dexing |
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| Institution: | Institute of Mathematics |
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| Abstract: | Under very general assumptions, the author proves that classical solutions of diagonal quasilinear hyperbolic systems in high dimensions with nontrival initial data with compact support must blow up in a finite time; In particular, for the case of small initial data with compact support, the author gives the life-span of classical solutions and its application to nonlinear wave equations. |
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| Keywords: | quasilinear wave equations blow-up life-span |
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