On convergence of solutions of fractal Burgers equation toward rarefaction waves
| dc.creator | Karch, Grzegorz | |
| dc.creator | Miao, Changxing | |
| dc.creator | Xu, Xiaojing | |
| dc.date | 2007-02-05 | |
| dc.date.accessioned | 2026-07-07T10:08:36Z | |
| dc.date.available | 2026-07-07T10:08:36Z | |
| dc.description | In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation $u_t+(-\partial^2_x)^{α/2} u+uu_x=0$ with $α\in (1,2)$ is studied. It is shown that if the nondecreasing initial datum approaches the constant states $u_\pm$ ($u_-<u_+$) as $x\to \pm\infty$, respectively, then the corresponding solution converges toward the rarefaction wave, {\it i.e.} the unique entropy solution of the Riemann problem for the nonviscous Burgers equation. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702088 | |
| dc.identifier | http://arxiv.org/abs/math/0702088 | |
| dc.identifier | SIAM J. MATH. ANAL.39(2008)1536-1549 | |
| dc.identifier | doi:10.1137/070681776 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171052 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 60J60, 35B40,35K55,35Q53 | |
| dc.title | On convergence of solutions of fractal Burgers equation toward rarefaction waves | |
| dc.type | text |