Mathematics Seminar 10/19/23

Abstract:  Understanding how and where the tumor starts is a central concern in the recent theory of cell-of-origin - the normal cell that acquires the first cancer-promoting genetic hit. In mathematical oncology focusing on brain tumors, reconstructing the primary site of tumor cells is an essential but challenging problem because of the natural ill-posedness and highly dynamic nonlinearities. In this talk, we present fundamental ideas to construct a new inversion called Variational Quasi-reversibility (VQR) to solve the source localization problem. As a PDE-based approach, this method relies on adding a suitable perturbing operator to the original PDE and, consequently, gaining the corresponding fine stabilized operator. In this way, the designated approximate problem is forward-like, whose weak solvability is guaranteed using the standard Faedo-Galerkin procedure. Moreover, relying on the energy-like analysis coupled with a suitable Carleman weight, convergence rates in a mixed topology of L²  - H¹ are obtained when the true solution is sufficiently smooth.

For more information, please contact:  Dr. Vu Thai Luan, luan@math.msstate.edu, (662)-325-7162