On approximation and error estimate for Poisson equation in Banach space

Abstract

This article investigates the Poisson equation inverse source problem. This is an ill-posed, i.e. a small change in the data will lead to a very large change in the solution. Therefore, a regularized solution is necessary. In this work, we construct the regularized solution by truncation method. We also investigate the convergent rate between the regularized solution and the sought solution in \(L^j(0,\pi)\).