郑全.对角型拟线性双曲组整体经典解的渐近行为[J].数学研究及应用,2010,30(1):29~40
对角型拟线性双曲组整体经典解的渐近行为
Asymptotic Behavior of Global Classical Solutions to Quasilinear Hyperbolic Systems of Diagonal Form
投稿时间:2008-04-07  最后修改时间:2008-04-16
DOI:10.3770/j.issn:1000-341X.2010.01.003
中文关键词:  对角型拟线性双曲组  弱线性退化  整体经典解  富有组  行波解.
英文关键词:quasilinear hyperbolic systems of diagonal form  weak linear degeneracy  global classical solution  rich system  traveling wave.
基金项目:教育部博士点基金(Grant No.20070246173).
作者单位
郑全 复旦大学数学科学学院, 上海 200433 
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中文摘要:
      本文主要研究具有弱线性退化特征的对角型拟线性双曲组整体经典解的渐近行为.在整体经典解存在的基础上,我们证明了当$t$趋向于无穷大时,经典解趋向于一组行波解的线性组合.
英文摘要:
      This paper deals with the asymptotic behavior of global classical solutions to quasilinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. On the basis of global existence and uniqueness of $C^1$ solution, we prove that the solution to the Cauchy problem approaches a combination of $C^1$ traveling wave solutions when $t$ tends to the infinity.
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