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

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.

authors

• Rundell, William

published proceedings

• INVERSE PROBLEMS

author list (cited authors)

• Jin, B., & Rundell, W.

citation count

• 122

complete list of authors

• Jin, Bangti||Rundell, William

publication date

• July 2012

publisher

• IOP Publishing  Publisher

published in

• Inverse Problems  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1088/0266-5611/28/7/075010

start page

• 075010

end page

• 075010

volume

• 28

issue

• 7

URL

• http://dx.doi.org/10.1088/0266-5611/28/7/075010