Hilbert空间中分数阶随机退化演化方程的指数稳定性和稳定性:从属原理

IF 1.3 4区 数学 Q1 MATHEMATICS
Arzu Ahmadova, N. Mahmudov, J. Nieto
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引用次数: 7

摘要

本文利用隶属原理和半群理论,得到了Hilbert空间中分数阶随机退化演化方程温和解的闭表示形式。我们研究了上述具有非线性状态相关项的抽象分数阶随机柯西问题,并证明了如果描述模型线性部分的Sobolev型解族是指数稳定的,那么在非线性的某些Lipschitz连续性假设下,整个系统保持这种性质。我们还建立了稳定性的条件,并证明了当稳定器作用于控制系统时,随机非线性分数阶柯西问题是指数可稳定的。最后,我们提供了应用程序来证明我们的理论的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space: Subordination principle
In this paper, we obtain a closed-form representation of a mild solution to the fractional stochastic degenerate evolution equation in a Hilbert space using the subordination principle and semigroup theory. We study aforesaid abstract fractional stochastic Cauchy problem with nonlinear state-dependent terms and show that if the Sobolev type resolvent families describing the linear part of the model are exponentially stable, then the whole system retains this property under some Lipschitz continuity assumptions for nonlinearity. We also establish conditions for stabilizability and prove that the stochastic nonlinear fractional Cauchy problem is exponentially stabilizable when the stabilizer acts linearly on the control systems. Finally, we provide applications to show the validity of our theory.
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来源期刊
Evolution Equations and Control Theory
Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.10
自引率
6.70%
发文量
5
期刊介绍: EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology
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