On convergence of solutions of fractal Burgers equation toward rarefaction waves

Grzegorz Karch, Changxing Miao, Xiaojing Xu

In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation $u_t+(-{\partial }_x^2{)}^{\alpha /2}u+u{u}_x=0$ with $\alpha \in (1,2)$ is…