ncku-talk2020-10-29

Colloquium

DATE 2020-10-29　15:10-16:00

PLACE 數學館3174教室

SPEAKER 林奕亘助理教授（交通大學數學系）

TITLE Monotonicity-Based Inversion of the Fractional Schrödinger Equation

ABSTRACT We consider an inverse problem for the fractional Schrödinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calderón problem in a constructive manner. Secondly, we offer a reconstruction method for an unknown obstacles in a given domain. Our method is independent of the dimension and only requires the background solution of the fractional Schrödinger equation.
學者簡介

Colloquium

DATE	2020-10-29　15:10-16:00

PLACE	數學館3174教室

SPEAKER	林奕亘助理教授（交通大學數學系）

TITLE	Monotonicity-Based Inversion of the Fractional Schrödinger Equation

ABSTRACT	We consider an inverse problem for the fractional Schrödinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calderón problem in a constructive manner. Secondly, we offer a reconstruction method for an unknown obstacles in a given domain. Our method is independent of the dimension and only requires the background solution of the fractional Schrödinger equation. 學者簡介