期刊
SIAM REVIEW
卷 53, 期 1, 页码 129-153出版社
SIAM PUBLICATIONS
DOI: 10.1137/100808836
关键词
Burgers equation; invariant manifolds; metastability; scaling variables; self-similar
资金
- NSF [DMS-1007450, DMS-0405724, DMS-0908093]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0908093] Funding Source: National Science Foundation
The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L-2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据