MathAmsud 08MATH04: Controllability and Inverse Problems in PDE's

AM2V Members: Eduardo Cerpa, Alberto Mercado
Start Date: 01-01-2009 - End Date: 12-31-2011
Status: in progress

Controllability and inverse problems for PDEs are strongly related topics. The principal objective of this project is to connect research groups in inverse and controllability theory working in France, Brazil and Chile. The main idea is to share know-how in both disciplines to deal with the study of two representative models: Schrodinger and Korteweg-de Vries (KdV) equations. More specifically, in this project, our aim is to study: 1. Control and inverse problems for the Korteweg-de Vries equation, including: existence of a minimal time for controllability, stabilization of both linear and nonlinear systems, bilinear control systems, source identification inverse problems, and numerical ill posed problems. 2. Control and inverse problems for the Schrodinger equation, including: sharp estimates of the minimal time for controllability, 2-D or 3-D moving potential wells, feedback approaches to generate new trajectories, systems of coupled Schrodinger equations, and inverse problems with partial boundary measurements. 3. Other controllability and inverse problems: fluid-structure problems, Lagrangian controllability, and transport dominated problems.

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