具有阻尼的随机弹性系统mild解的存在性  

Existence of mild solutions for elastic systems with damping

作　　者：范虹霞[1] 张小云 FAN Hongxia;ZHANG Xiaoyun(Collage of mathematics and physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《兰州交通大学学报》2025年第1期49-54,共6页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(11561040)。

摘　　要：在实际的阻尼弹性系统的应用中,研究的模型受到白噪声或周围环境的影响而产生一些变化,这些随机因素会影响模型的运行结果。相较于传统的阻尼弹性系统,这类系统因融入了随机项而显得更为复杂,给理论研究带来了极大的困难。为了攻克这一难题,本文将采用随机分析这一工具,在Hilbert空间中对具有阻尼的随机弹性系统mild解的存在性结果进行深入探讨。在具体的研究过程中,我们首先巧妙地运用了单调迭代技巧和算子半群理论,成功构建了所研究系统的mild解。这一步骤为后续的深入分析奠定了坚实的理论基础。随后,在非线性项非Lipschitz连续的情况下,进一步利用随机分析理论、Holder不等式和不动点定理,经过一系列严谨的推导和论证,最终得出了所研究系统mild解的存在性结果。这一成果,是对阻尼弹性系统现有理论的重要补充与拓展。In practical applications of damped elastic systems,the model under investigation is influenced by variations caused by white noise and environmental factors.These stochastic elements can significantly affect the outcomes of model simulations.Compared to traditional damped elastic systems,this type of system is more complex due to the inclusion of stochastic terms,which presents considerable challenges for theoretical analysis.In order to address this challenge,this paper will employ stochastic analysis as a tool to provide insights into the existence of mild solutions for stochastic elastic systems with damping in Hilbert space.In the specific research process,we first skillfully employ the monotone iteration technique and operator semigroups theory to construct the mild solution of the system under investigation.This initial step establishes a solid theoretical foundation for the subsequent in depth analysis.Following this,we utilize stochastic analysis theory,Holder inequality,and the fixed point theorem to address the case of non Lipschitz continuity of the nonlinear terms.After a series of rigorous derivations and arguments,we ultimately obtain the existence result of the mild solution for the studied system.This finding significantly supplements and extends the existing theory of damped elastic systems.

关 键 词：随机弹性系统 MILD解 阻尼 算子半群 

分 类 号：O175.15[理学—数学]