MATJ5110 MA1: The Boundary Control Method and Inverse Problems for the Wave Equation (JSS31) (2 cr)
In an inverse boundary value problem the task is to reconstruct the coefficients of a partial differential operator from the Dirichlet and Neumann boundary data of all solutions. The simplest version of such an operator is a familiar operator like the Laplacian or the wave operator plus an unknown potential, and then the task is to uniquely determine the potential from the boundary data. This course focuses on the boundary control method introduced by Belishev for solving this inverse problem for perturbations of the wave equation with full or partial data.
Students familiarize themselves with inverse boundary value problems, especially of the hyperbolic type. They also learn the fundamentals of the boundary control method and the role it plays in the study of such problems.
Description of prerequisites
Familiarity with partial differential equations and functional analysis.
Participation in teaching (2 cr)
Lectures and exercises. Mandatory class attendance and assignments.