Asymptotics toward strong rarefaction waves for \(2\times 2\) systems of viscous conservation laws (Q1770159)

The authors studied the time asymptotic behavior of the solution to general systems of \(2\times 2\) viscous conservation laws with positive viscosity coefficient matrix. The initial data \(u_0(x)\) have limit \(u_\pm\) as \(x\) tends to infinity. Assume that the Riemann problem for corresponding hyperbolic conservation laws with initial data \(u^r_0(x)= \begin{cases} u_-,\,x< 0\\ u_+,\,x> 0\end{cases}\) can be solved by one rarefaction wave. The authors show that the Cauchy problem for above viscous conservation laws admits a unique global smooth solution \(u(t, x)\), which tends to \(u_0^r(t, x)\) as \(t\) tends to infinity. Here no smallness on \(|u_+- u_-|\) is required.