Identification of the pollution source of a parabolic equation with the time-dependent heat conduction

Abstract

We consider the problem of identifying the pollution source of a 1D parabolic equation from the initial and the final data. The problem is ill posed and regularization is in order. Using the quasi-boundary method and the truncation Fourier method, we present two regularization methods. Error estimates are given and the methods are illustrated by numerical experiments. © 2014 Tuan et al.; licensee Springer.