Asymptotic behavior of global classical solutions of quasilinear hyperbolic systems

We study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with weakly linearly degenerate characteristic fields. Based on the existence results on the global classical solution, we prove that, when t tends to infinity, the solution approaches a combination of C¹ travelling wave solutions at algebraic rate (1 + t)^-μ, provided that the initial data decay at the rate (1 + |x|)^-(1+μ) as x tends to ±∞, where μ, is a positive constant.