A Filippov approximation theorem for strengthened one-sided Lipschitz differential inclusions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-11 DOI:10.1007/s10589-023-00517-9

Robert Baier, Elza Farkhi

引用次数: 1

Abstract

Abstract We consider differential inclusions with strengthened one-sided Lipschitz (SOSL) right-hand sides. The class of SOSL multivalued maps is wider than the class of Lipschitz ones and a subclass of the class of one-sided Lipschitz maps. We prove a Filippov approximation theorem for the solutions of such differential inclusions with perturbations in the right-hand side, both of the set of the velocities (outer perturbations) and of the state (inner perturbations). The obtained estimate of the distance between the approximate and exact solution extends the known Filippov estimate for Lipschitz maps to SOSL ones and improves the order of approximation with respect to the inner perturbation known for one-sided Lipschitz (OSL) right-hand sides from $$\frac{1}{2}$$ 1 2 to 1.

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强化单侧Lipschitz微分包涵的Filippov近似定理

摘要:我们考虑具有增强单侧Lipschitz (SOSL)右手边的微分内含物。SOSL多值映射类比Lipschitz映射类更宽，是单侧Lipschitz映射类的一个子类。我们证明了这类微分包体的解的Filippov近似定理，其右边既有速度集(外摄动)，也有状态集(内摄动)。得到的近似解和精确解之间距离的估计将已知的Lipschitz映射的Filippov估计扩展到SOSL映射，并将关于单侧Lipschitz (OSL)右手边已知的内部扰动的近似阶数从$$\frac{1}{2}$$ 1 2提高到1。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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