Dynamics of Stochastic Reaction-Diffusion Equations
Dynamics of Stochastic Reaction-Diffusion Equations
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DOI：
10.1142/9789811209796_0001
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
C. Kuehn;A. Neamţu
中科院分区：
文献类型：
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作者：
C. Kuehn;A. Neamţu
随机偏微分方程（SPDE）是一个非常活跃的研究领域，最近有许多新的发展和突破性的成果。有几种成熟的方法和途径用于构造SPDE的解，由于扰动方程的噪声项的不规则性，这总是一个挑战。在应用中，这样的噪声项可以量化某些参数的知识的缺乏，有限尺寸效应，和/或由于外部扰动而发生的波动。由于随机偏微分方程已经成为一种重要的建模工具，人们对研究其动力学现象的兴趣越来越大。这项工作的主要目标是提供一个调查的不同方法的解决方案理论和动力学性质的SPDES，这是一个广泛的社会感兴趣的现代方法在随机分析，动力学和应用。
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for SPDEs, which is always a challenge due to the irregularity of the noise terms that perturb the equation. In applications, such noise terms can quantify the lack of knowledge of certain parameters, finite-size effects, and/or fluctuations occurring due to external perturbations. Since SPDEs have become a key modelling tool in applications, there has been a growing interest in studying their dynamical phenomena. The main goal of this work is to provide a survey on different approaches to solution theory and dynamical properties for SPDEs, which is accessible for a wide community interested in modern methods in stochastic analysis, dynamics and applications.