Multidimensional Stability of Planar Traveling Waves for Stochastically Perturbed Reaction–Diffusion Systems

IF 2.3 2区 数学 Q1 MATHEMATICS, APPLIED
M. van den Bosch, H. J. Hupkes
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引用次数: 0

Abstract

We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales that are exponentially long with respect to the noise strength. This is achieved by means of a stochastic phase-tracking mechanism that can be maintained over such long timescales. The corresponding mild formulation of our problem features stochastic integrals with respect to anticipating integrands, which hence cannot be understood within the well-established setting of Itô-integrals. To circumvent this problem, we exploit and extend recently developed theory concerning forward integrals.

Abstract Image

随机摄动反应扩散系统平面行波的多维稳定性
我们考虑在二维或更高维度的空间域上具有乘性噪声的反应扩散系统。噪声过程在时间上是白色的,在空间上是彩色的,在平移下是不变的。受前人实线研究的启发,我们在相对于噪声强度呈指数长的时间尺度上建立了柱面域上平面波的多维稳定性。这是通过一种随机相位跟踪机制来实现的,这种机制可以在如此长的时间尺度上保持不变。我们的问题的相应温和的公式具有相对于预期积分的随机积分,因此不能在Itô-integrals的既定设置中理解。为了避免这个问题,我们利用和推广了最近发展起来的关于正积分的理论。
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来源期刊
Studies in Applied Mathematics
Studies in Applied Mathematics 数学-应用数学
CiteScore
4.30
自引率
3.70%
发文量
66
审稿时长
>12 weeks
期刊介绍: Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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