| 郭飞.具常重特征的非齐次拟线性双曲组的整体弱间断解[J].数学研究及应用,2012,32(6):699~714 |
| 具常重特征的非齐次拟线性双曲组的整体弱间断解 |
| Global Weakly Discontinuous Solutions for Inhomogeneous Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity |
| 投稿时间：2011-02-08 修订日期：2011-09-01 |
| DOI：10.3770/j.issn:2095-2651.2012.06.010 |
| 中文关键词: 非齐次拟线性双曲组 常重特征 初值问题 整体弱间断解 弱线性退化 匹配条件. |
| 英文关键词:inhomogeneous quasilinear hyperbolic system characteristic with constant multiplicity Cauchy problem global weakly discontinuous solution weak linear degeneracy matching condition. |
| 基金项目:国家自然科学基金资助项目(Grant No.11071141, 11271192), 中国博士后科研资助基金(Grant No.20100481161), 江苏省博士后科研资助计划(Grant No.1001042C), 江苏省青蓝工程; 江苏省高校自然科学基础研究项目(Grant No.11KJA110001), 江苏省基础研究计划(自然科学基金) (Grant No.BK2011777). |
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| 中文摘要: |
| 本文主要研究具有常重特征的非齐次拟线性双曲组的初值问题, 所考虑的初始资料是非光滑的.在匹配条件之下, 利用一个精细的波的分解公式, 得到了此初值问题存在唯一的整体弱间断解的充要条件. |
| 英文摘要: |
| This paper considers the Cauchy problem with a kind of non-smooth initial data for general inhomogeneous quasilinear hyperbolic systems with characteristics with constant multiplicity. Under the matching condition, based on the refined fomulas on the decomposition of waves, we obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution to the Cauchy problem. |
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