Speaker
Description
We address two inverse source problems when determining a space-dependent source term and a time-dependent coefficient for a two-dimensional generalized diffusion equation. These problems are ill-posed in the Hadamard sense, where small perturbations in the data can lead to uncontrolled variations in the solution. From a analytic viewpoint we provide existence and uniqueness results for the solutions of these problems under appropriate over-specified and regularity conditions. From a computational viewpoint, we use a quasi-boundary value regularization to reconstruct the underlying approximate source term. In the reconstruction, by employing a finite difference discretization of the regularized problem, we encounter a two-by-two (structured) block linear system. We propose efficient (preconditioned) Krylov solvers and we present numerical experiments to demonstrate the effectiveness of our method.
- A. Ilyas, S. A. Malik, Direct and some inverse problems for a generalized diffusion equation with variable coefficients, Computational and Applied Mathematics, 43(6), (2024), 364 pp.
- H.-K. Pang, H.-H. Qin, S. Ni, Sine transform based preconditioning for an inverse source problem of time-space fractional diffusion equations. Journal of Scientific Computing, 100(3), Paper No. 74,(2024), 32 pp.
- C. Garoni, S. Serra-Capizzano, Generalized locally Toeplitz sequenecs: theory and applications, Vol. II, Springer, Cham, 2018.
- A. Ilyas, S. Serra-Capizzano, Inverse Source Problems for Identifying Time and Space-Dependent Coefficients in a 2D Generalized Diffusion Equation, preprint 2024.
