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 - <p>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.</p>