Convergence rate of the solution toward boundary layer solution for initial-boundary value problem of the 2-D viscous conservation laws

摘要

In this paper, we study the large time behavior of the solution to the initial boundary value problem for 2-D viscous conservation laws in the space x ⩾ bt. The global existence and the asymptotic stability of a stationary solution are proved by Kawashima et al. [1]. Here, we investigate the convergence rate of solution toward the boundary layer solution with the non-degenerate case where f′(u+) − b < 0. Based on the estimate in the H2 Sobolev space and via the weighted energy method, we draw the conclusion that the solution converges to the corresponding boundary layer solution with algebraic or exponential rate in time, under the assumption that the initial perturbation decays with algebraic or exponential in the spatial direction.