Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
复制标题
Swift-Hohenberg 方程空间周期解的扩散稳定性
DOI：
10.1007/bf02108820
复制
发表时间：
1996
影响因子：
2.4
通讯作者：
G. Schneider
中科院分区：
文献类型：
--
作者：
G. Schneider
我们对Swift-Hohenberg方程在无穷线上关于小可积扰动的eckhaus稳定平衡点的非线性稳定性很感兴趣。显示这些平稳解的稳定性的困难在于它们的线性化具有一直到零的连续谱。用重整化理论处理非线性稳定性问题，证明了非线性项是不相关的，即完全非线性问题表现为扩散域下的线性化问题的渐近行为。
We are interested in the nonlinear stability of the Eckhaus-stable equilibria of the Swift-Hohenberg equation on the infinite line with respect to small integrable perturbations. The difficulty in showing stability for these stationary solutions comes from the fact that their linearizations possess continuous spectrum up to zero. The nonlinear stability problem is treated with renormalization theory which allows us to show that the nonlinear terms are irrelevant, i.e. that the fully nonlinear problem behaves asymptotically as the linearized one which is under a diffusive regime.