On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation

Abstract

In this paper, we consider the Cauchy problem for the Helmholtz equation in a rectangle, where the Cauchy data is given for y = 0 and boundary data are for x = 0 and x = π . The solution is sought in the interval 0 < y ≤ 1 . A quasi-reversibility method is applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates.