Abstract
This paper is devoted to identify a time-dependent source term in a time–space fractional diffusion equation by using the usual initial and boundary data and an additional measurement data at an inner point. The existence and uniqueness of a weak solution for the corresponding direct problem with homogeneous Dirichlet boundary condition are proved. We provide the uniqueness and a stability estimate for the inverse time-dependent source problem. Based on the separation of variables, we transform the inverse source problem into a first kind Volterra integral equation with the source term as the unknown function and then show the ill-posedness of the problem. Further, we use a boundary element method combined with a generalized Tikhonov regularization to solve the Volterra integral equation of the fist kind. The generalized cross validation rule for the choice of regularization parameter is applied to obtain a stable numerical approximation to the time-dependent source term. Numerical experiments for six examples in one-dimensional and two-dimensional cases show that our proposed method is effective and stable.
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.