BEHAVIOR OF SOLUTIONS FOR RADIALLY SYMMETRIC SOLUTIONS FOR BURGERS EQUATION WITH A BOUNDARY CORRESPONDING TO THE RAREFACTION WAVE

Abstract We investigate the large-time behavior of the radially symm etric solution for Burgers equation on the exterior of a small ball in multi-dim ensional space, where the boundary data and the data at the far field are prescribed. In a previous paper [1], we showed that, for the case in which the boundary data is equal to 0 or negative, the asymptotic stability is the same as that for the vis cou conservation law. In the present paper, it is proved that if the boundary data is po sitive, the asymptotic state is a superposition of the stationary wave and the raref action wave, which is a new wave phenomenon. The proof is given using a standard L2 energy method and the characteristic curve method.