Asymptotic behavior of radially symmetric solutions for the Burgers equation in several space dimensions

We study large-time behavior of the radially symmetric solution for the Burgers equation on the exterior of a ball in a multi dimensional space, where boundary data at the far field are prescribed. Liu et al. (1998) considered the asymptotic behavior of the solution of scalar viscous conservation law for the case where the corresponding Riemann problem for the hyperbolic part admits a rarefaction wave. In the present paper, it is proved that for a radially symmetric solution to the Burgers equation on a multidimensional space, the asymptotic behaviors are the same as in Liu et al. (1998). Furthermore, we also derive the time convergence rate. The proof is given by a standard L2L2 energy method and a time weighted energy method.