期刊
KINETIC AND RELATED MODELS
卷 12, 期 5, 页码 1093-1108出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2019041
关键词
Transport equation in the space of Radon measures; bounded Radon measures; differentiability with respect to the parameter
资金
- Polish Government MNiSW
- National Science Centre, Poland [UMO-2015/18/M/ST1/00075]
- National Science Centre [DEC-2012/05/E/ST1/02218]
We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differentiable with respect to the perturbation parameter in a proper Banach space, which is predual to the Holder space C1+alpha (R-d). This result on differentiability is necessary for application in optimal control theory, which we also discuss.
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