TY - JOUR T1 - Asymptotic Behavior of Global Classical Solutions to a Kind of Mixed Initial-boundary Value Problem JO - Journal of Partial Differential Equations VL - 2 SP - 114 EP - 130 PY - 2007 DA - 2007/05 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5297.html KW - Quasilinear hyperbolic system KW - Global classical solution KW - Asymptotic behavior KW - Weak linear degeneracy KW - Normalized coordinates KW - Travelling wave AB -

We study the asymptotic behavior of global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Based on the existence results on the global classical solutions given by Li and Wang in [1] and employing the method of Kong and Yang in [2], we prove that, when t tends to infinity, the solution approaches a combination of C¹ travelling wave solutions at the algebraic rate (1+t)^{-μ}, provided that the initial data decay at the rate (1+x)^{-(1+μ)} as x tends to +∞ and the boundary data decay at the rate (1+t)^{-(1+μ)} as t tends to +∞, where μ is a positive constant.