On convergence of solutions of fractal burgers equation toward rarefaction waves

In this paper, the large time behavior of solutions of the Cauchy problem for the one-dimensional fractal Burgers equation u(t) +(-partial derivative(2)(x))(alpha/2) u + uu(x) = 0 with alpha = (1, 2) is studied. It is shown that if the nondecreasing initial datum approaches the constant states u +/- (u(-) < u(+)) as x -> +/-infinity, respectively, then the corresponding solution converges toward the rarefaction wave, i.e., the unique entropy solution of the Riemann problem for the nonviscous Burgers equation.