Mathematics Colloquium: Pointwise Carleman estimates for Schrödinger equations on Riemannian manifolds and Control theo

2007-02-09

4:10 pm, Neill Hall 5W

Xiangjin Xu

Abstract: I will present pointwise Carleman estimates without lower order terms for general non-conservative Schrödinger equations defined on an n-dimensional Riemannian manifold. As a consequence, we obtain the global uniqueness, continuous observability and stabilization results for Schrödinger equations with Dirichlet boundary condition or Neumann boundary condition. Results for the Euler-Bernoulli equations with “hinged” boundary condition are also discussed. Some future research on this ongoing program will be discussed. The presented work is part of the ongoing program with Professor Irena Lasiecka and Professor Roberto Triggiani at the University of Virginia. The talk is intended for a mathematically-literate audience.