An inverse problem for a one-dimensional time-fractional diffusion problem

Bangti Jin, William Rundell

Research output: Contribution to journalArticlepeer-review

113 Scopus citations

Abstract

We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L 2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented. © 2012 IOP Publishing Ltd.
Original languageEnglish (US)
Pages (from-to)075010
JournalInverse Problems
Volume28
Issue number7
DOIs
StatePublished - Jun 26 2012
Externally publishedYes

Fingerprint Dive into the research topics of 'An inverse problem for a one-dimensional time-fractional diffusion problem'. Together they form a unique fingerprint.

Cite this