带斯蒂尔杰斯导数的状态相关扫频过程

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-07-26 DOI:10.1007/s00245-024-10169-8

Bianca Satco, George Smyrlis

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引用次数: 0

摘要

我们证明了受状态相关凸移动集的扫频过程控制的扰动微分包含的解的存在性，该过程在N_{C(t,u(t))}(u(t))+F(t,u(t)),/; \mu _g-a.u(0)=u_0\in C(0,u_0).\end{array}\right.\end{aligned}$$我们的研究带来的新颖之处在于Stieltjes导数$u'_g$相对于一个右连续非递减函数$g:[0,T]\rightarrow {\mathbb {R}}$的参与，从而建立了一个包含ODEs、脉冲微分问题、时间尺度上的动态夹杂或广义微分问题的非常宽泛的框架。这里 $\mu _g$ 是与 g 相关的 Stieltjes 量，\(N_{C(t,u(t))}(u(t))表示 C(t, u(t)) 在点 u(t) 处的法锥。）

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State-Dependent Sweeping Processes with Stieltjes Derivative

We prove the existence of solutions for a perturbed differential inclusion governed by a sweeping process with state dependent convex moving set

$$\begin{aligned}\left\{ \begin{array}{l} -u'_g(t)\in N_{C(t,u(t))}(u(t))+F(t,u(t)),\; \mu _g-a.e. \; t\in (0,T]\\ u(0)=u_0\in C(0,u_0). \end{array} \right. \end{aligned}$$

The novelty brought by our study is the involvement of the Stieltjes derivative $u'_g$ with respect to a right-continuous nondecreasing function $g:[0,T]\rightarrow {\mathbb {R}}$, thus establishing a very wide framework containing ODEs, impulsive differential problems, dynamic inclusions on time scales or generalized differential problems. Here $\mu _g$ is the Stieltjes measure associated to g and $N_{C(t,u(t))}(u(t))$ denotes the normal cone of C(t, u(t)) at the point u(t).

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.