On convergence of solutions of fractal Burgers equation toward rarefaction waves

Details On convergence of solutions of fractal Burgers equation toward rarefaction waves On convergence of solutions of fractal Burgers equation toward rarefaction waves

2007-02-05

arxiv.org/abs/math/0702088v1

SIAM J. MATH. ANAL.39(2008)1536-1549

Mathematics

Analysis of PDEs

15 pages

Scientific paper

10.1137/070681776

In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation $u_t+(-\partial^2_x)^{\alpha/2} u+uu_x=0$ with $\alpha\in (1,2)$ is studied. It is shown that if the nondecreasing initial datum approaches the constant states $u_\pm$ ($u_-

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