Uniquely identifying the variable order of time-fractional partial differential equations on general multi-dimensional domains. Issue 10 (3rd October 2021)

• Record Type: Journal Article
• Authors: Zheng, Xiangcheng; Wang, Hong
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 10(2021)
• Page Start: 1401
• Page End: 1411
• Publication Date: 2021-10-03
• Subjects: Determination of variable order -- variable-order time-fractional diffusion equation -- inverse problem -- uniqueness -- variable diffusivity; 35R30; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2020.1849182
• Languages: English
• ISSNs: 1741-5977

Abstract

ABSTRACT: We proved the unique determination of the variable order in a two-scale mobile–immobile variable-order time-fractional partial differential equation with a variable diffusivity tensor imposed on a general multi-dimensional domain, with the observations of the unknown solutions on any arbitrarily small spatial domain over a sufficiently small time interval. The proved theorem provides a guidance where the measurements should be performed and ensures that with these observations the uniqueness of the identification is theoretically guaranteed.