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GCOE Seminars
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
2010/12/22
11:00-12:00 Room #570 (Graduate School of Math. Sci. Bldg.)
Mourad Bellassoued (Faculté des Sciences de Bizerte)
Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map (ENGLISH)
Mourad Bellassoued (Faculté des Sciences de Bizerte)
Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map (ENGLISH)
[ Abstract ]
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).
