论文标题
在真实的金茨堡 - landau方程式中，定期卷解决方案的非线性稳定性针对$ c _ {\ mathrm {ub}}}^m $ - 付费
Nonlinear stability of periodic roll solutions in the real Ginzburg-Landau equation against $C_{\mathrm{ub}}^m$-perturbations
论文作者
论文摘要
真正的金茨堡 - 兰道方程是一种通用振幅方程式，用于描述表现出图灵分叉的模式形成系统。它具有空间周期性的滚动溶液，已知在局部扰动上是稳定的。本文的目的是证明其在有限的扰动上的稳定性，这不一定是本地化的。由于所有最先进的技术都依赖于扰动的本地化或周期性属性，因此我们开发了一种新方法，该方法仅采用纯$ l^\ infty $ - 估算。通过完全利用线性化产生的半群的平滑性能，尽管衰减速率较慢，我们仍能够关闭非线性迭代。为了显示我们方法的更广泛相关性，我们还将其应用于振幅方程，因为它似乎是具有额外保护定律的模式形成系统。
The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially periodic roll solutions which are known to be stable against localized perturbations. It is the purpose of this paper to prove their stability against bounded perturbations, which are not necessarily localized. Since all state-of-the-art techniques rely on localization or periodicity properties of perturbations, we develop a new method, which employs pure $L^\infty$-estimates only. By fully exploiting the smoothing properties of the semigroup generated by the linearization, we are able to close the nonlinear iteration despite the slower decay rates. To show the wider relevance of our method, we also apply it to the amplitude equation as it appears for pattern-forming systems with an additional conservation law.
