2018/10/03 by Mourad Bellassoued, Bellassoued, Mourad, Ibtissem Ben Aïcha +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1810.01976
openalex publication_date 2018/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, we consider a non self adjoint hyperbolic operator with\na vector field and an electric potential that depend not only on the space\nvariable but also on the time variable. More precisely, we attempt to stably\nand simultaneously retrieve the real valued velocity field and the real valued\npotential from the knowledge of Neumann measurements performed on the whole\nboundary of the domain. We establish in dimension n greater than two, stability\nestimates for the problem under consideration. Thereafter, by enlarging the set\nof data we show that the unknown terms can be stably retrieved in larger\nregions including the whole domain. The proof of the main results are mainly\nbased on the reduction of the inverse problem under investigation to an\nequivalent and classic inverse problem for an electro-magnetic wave equation.\n