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An inverse source problem for a two dimensional time fractional diffusion equation with nonlocal boundary conditions
Author(s) -
Kirane Mokhtar,
Malik Salman A.,
AlGwaiz Mohammed A.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2661
Subject(s) - mathematics , biorthogonal system , eigenfunction , inverse problem , uniqueness , mathematical analysis , inverse , diffusion equation , boundary value problem , diffusion , space (punctuation) , eigenvalues and eigenvectors , geometry , wavelet , thermodynamics , linguistics , physics , wavelet transform , economy , philosophy , quantum mechanics , artificial intelligence , computer science , economics , service (business)
We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L 2 [(0,1) × (0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data. Copyright © 2012 John Wiley & Sons, Ltd.