A local sensitivity analysis for the kinetic Cucker-Smale equation with random inputs

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Ha, Seung-Yeal^1,2,3  Jin, Shi⁴  Jung, Jinwook¹ 

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[3] Korea Inst Adv Study, Hoegiro 87, Seoul 02455, South Korea

[4] Univ Wisconsin, Dept Math Sci, Madison, WI 53706 USA

关键词: Cucker-Smale model;    Flocking;    Local sensitivity analysis;    Random communication;    Uncertainty quantification;   

DOI  :  10.1016/j.jde.2018.05.013

来源: Elsevier

【 摘 要 】

We present a local sensitivity analysis for the kinetic Cucker-Smale (C-S) equation with random inputs. This is a companion work to our previous local sensitivity analysis for the particle C-S model. Random inputs in the coefficients of the kinetic C-S equation can be caused by diverse sources such as the incomplete measurement and interactions with unknown environments, and will enter the problem through the communication function or initial data. For the proposed random kinetic C-S equation, we present sufficient conditions for the pathwise well-posedness and flocking estimates. For the local sensitivity analysis, we study the propagation of regularity of the kinetic density function in random space. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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