Inverse Source Problem for advection-diffusion equations from boundary measured data

Abstract

Direct and inverse boundary value problems for diffusion equations with advection terms are widely used for mathematical modelling of natural and technological processes [1, 2, 5-20]. The analytical methods for finding solutions to direct diffusion-advection problems have been studied intensively [6, 7, 10] and much of the present effort is directed towards the speed and accuracy of computational implementations of numerical techniques [18-20] rather than further theoretical developments. On the other hand, the study of the corresponding inverse source problems has raised a lot of interest lately mainly due to their many practical applications including the detection of pollution sources in an environmental medium ([7-17]).