Asymptotics toward strong rarefaction waves for 2 × 2 systems of viscous conservation laws

This paper concerns the time asymptotic behavior toward large rarefaction waves of the solution to general systems of 2 × 2 hyperbolic conservation laws with positive viscosity coefficient B(u) 8 <ut + F(u)_x = (B(u)u_x)_x, u ∈ R², : u(0,x) = u ₀(x) → u± as x → ±∞. Assume that the corresponding Riemann problem 8 u_t + F(u)_x = 0, ( u _-1, x <0, u(0,x) = u₀^r(x) = u+, x > 0 can be solved by one rarefaction wave. If u₀(x) in (*) is a small perturbation of an approximate rarefaction wave constructed in Section 2, then we show that the Cauchy problem (*) admits a unique global smooth solution u(t, x) which tends to u^r(t, x) as the t tends to infinity. Here, we do not require |u₊- - u_-| to be small and thus show the convergence of the corresponding global smooth solutions to strong rarefaction waves for 2 × 2 viscous conservation laws.