An undetermined coefficient problem for a fractional diffusion equation. (18th December 2015)

• Record Type: Journal Article
• Authors: Zhang, Zhidong
• Is Part Of: Inverse problems. Volume 32:Number 1(2016:Jan.)
• Publication Date: 2015-12-18
• Subjects: fractional diffusion -- fractional inverse problem -- reconstruct diffusion coefficient -- uniqueness -- monotonicity -- iteration algorithm; 35R11 -- 35R30 -- 65M32; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/1/015011
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider a fractional diffusion equation (FDE) with an undetermined time-dependent diffusion coefficient a ( t ). Firstly, for the direct problem part, we establish the existence, uniqueness and some regularity properties of the weak solution for this FDE with a fixed Secondly, for the inverse problem part, in order to recover we introduce an operator and show its monotonicity. With this property, we establish the uniqueness of a ( t ) and create an efficient reconstruction algorithm to recover this coefficient.