Nonlinear stability of fast invading fronts in a Ginzburg–Landau equation with an additional conservation law
Nonlinear stability of fast invading fronts in a Ginzburg–Landau equation with an additional conservation law
复制标题
具有附加守恒定律的 Ginzburg-Landau 方程中快速入侵前沿的非线性稳定性
DOI：
10.1088/1361-6544/abd612
复制
发表时间：
2021
期刊：
影响因子：
1.7
通讯作者：
Bastian Hilder
中科院分区：
文献类型：
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作者：
Bastian Hilder
我们考虑一类具有附加守恒律的Ginzburg-Landau方程中连接入侵态和不稳定基态的行波前解。对于具有守恒律结构的图灵图案形成系统，该系统表现为一般的振幅方程，例如Bénard-Marangoni问题。我们证明了足够快的前锋相对于前锋指数局部化的扰动的非线性稳定性。证明是基于在前锋前面使用指数权来稳定基态。主要的挑战是缺乏比较原理和入侵态只是扩散稳定的事实，即入侵态的扰动在时间上以多项式衰减。
We consider traveling front solutions connecting an invading state to an unstable ground state in a Ginzburg–Landau equation with an additional conservation law. This system appears as the generic amplitude equation for Turing pattern forming systems admitting a conservation law structure such as the Bénard–Marangoni problem. We prove the nonlinear stability of sufficiently fast fronts with respect to perturbations which are exponentially localized ahead of the front. The proof is based on the use of exponential weights ahead of the front to stabilize the ground state. The main challenges are the lack of a comparison principle and the fact that the invading state is only diffusively stable, i.e. perturbations of the invading state decay polynomially in time.