Numerical exact controllability of the 1D heat equation: duality and Carleman weights (Q467484)

The paper presents a design and analysis of a numerical algorithm for the null controllability of the 1D heat equation with locally supported distributed controls. With a brief overview of the Carleman type estimates, the paper apply the Fenchel-Rockafellar duality theory to an external problem. Some approximations are introduced to convert the extermal problem into a to well posed dual problem. It also designed an algorithm to couple the conjugate gradient method with the finite difference and finite element techniques. Numerical examples are illustrated to demonstrate the method. There are several theorems proved to develop the algorithm.