Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation

Abstract

An inverse boundary value problem for the 1+1 dimensional wave equation (partial derivative(2)(t) - c(x)(2)partial derivative(2)(x))u(x,t) = 0, x is an element of R+ is considered. We give a discrete regularization strategy to recover wave speed c(x) when we are given the boundary value of the wave, u(0,t), that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed (c) over tilde, satisfying a Holder type estimate parallel to (c) over tilde - c parallel to