Abstract
Consider a linear inverse problem of determining the space-dependent source term in a diffusion equation with time fractional order derivative from the flux measurement specified in partial boundary. Based on the analysis on the forward problem and the adjoint problem with inhomogeneous boundary condition, a variational identity connecting the inversion input data with the unknown source function is established. The uniqueness and the conditional stability for the inverse problem are proven by weak unique continuation and the variational identity in some norm. The inversion scheme minimizing the regularizing cost functional is implemented by using conjugate gradient method, with numerical examples showing the validity of the proposed reconstruction scheme.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Acta Mathematicae Applicatae Sinica, English Series
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
