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| Asymptotic Behavior of Global Classical Solutions of Quasilinear Non-strictly Hyperbolic Systems with Weakly Linear Degeneracy |
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Citation： |
Wenrong DAI.Asymptotic Behavior of Global Classical Solutions of Quasilinear Non-strictly Hyperbolic Systems with Weakly Linear Degeneracy[J].Chinese Annals of Mathematics B,2006,27(3):263~286 |
| Page view： 1138
Net amount： 957 |
Authors： |
Wenrong DAI; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10371073). |
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| Abstract： |
In this paper, we study the asymptotic behavior of global
classical solutions of the Cauchy problem for general quasilinear
hyperbolic systems with constant multiple and weakly linearly
degenerate characteristic fields. Based on the existence of global
classical solution proved by Zhou Yi et al., we show that, when
$t$ tends to infinity, the solution approaches a combination of
$C^{1}$ travelling wave solutions, provided that the total
variation and the $L^1$ norm of initial data are sufficiently
small. |
Keywords： |
Asymptotic behavior, Characteristic fields with constant multiplicity,
Weakly linear degeneracy, Global classical solution, Normalized coordi-
nates, Travelling wave |
Classification： |
35L45, 35L60, 35L40 |
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