Abstract
Facing application in real world, a simultaneous identification problem of determining the initial diffusion time (or the length of diffusion time) and source term in a time-fractional diffusion equation is investigated. Firstly, the simultaneous reconstruction problem is proposed by translating the Caputo fractional derivative. Then the uniqueness results for the simultaneous identification problem are proven by the technique of analytic continuation and the Laplace transformation method. Next, the Lipschitz continuousness of the observation operator is derived, and an alternating direction inversion algorithm is proposed to solve the simultaneous identification problem. At last, several numerical examples are computed to show the efficiency and stability of the reconstruction algorithm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.