A parabolic inverse convection–diffusion–reaction problem solved using space–time localization and adaptivity

Abstract

This paper investigates the solution of a parabolic inverse problem based upon the convection–diffusion–reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location: while in the first case the problem is solved using a Projected Damped Gauss Newton (PDGN), in the second one it is ill-posed and an adaptive parametrization with space–time localization will be adopted to regularize it.