| Asymptotic Behavior of Global Classical Solutions to the Cauchy Problem on a Semi-Bounded Initial Axis for Quasilinear Hyperbolic Systems |
| Received:April 04, 2008 Revised:April 16, 2008 |
| Key Words:
quasilinear hyperbolic system Cauchy problem on a semi-bounded initial axis global classical solution weak linear degeneracy matching condition travelling wave.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10771038). |
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| Abstract: |
| In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when $t$ tends to the infinity, the solution approaches a combination of $C^1$ travelling wave solutions with the algebraic rate $(1 t)^{-\mu}$, provided that the initial data decay with the rate $(1 x)^{-(1 \mu)}$ (resp. $(1-x)^{-(1 \mu)}$) as $x$ tends to $ \infty$ (resp. $-\infty$), where $\mu$ is a positive constant. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.01.004 |
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