DIRECT AND INVERSE PROBLEMS FOR THE LINEAR CONVECTIVE DIFFUSION EQUATION GOVERNING MIGRATION OF GROUND WATER POLLUTION
Ivan Dimov, Petko Ivanov Lalov · 2005
ABSTRACT. In this paper one dimensional migration of ground water pollution has been considered. For the linear convective diffusion equation governing of this phenomenon are posed and solved in the domain {0≤x< ∞ ; 0≤t≤T}the next problems: 1. Direct problem. At the initial moment, when the filtration flow is not polluted, a pollutant source starts to act c(0,t)=f(t) at x=0. We seek for the pollution distribution downstream. 2. Inverse problem For the measured pollution at point x=L, i.e. c(L,t), let us determine the characteristics of the pollution source c(0,t)=f(t). 3. Inverse coefficient problem For measured c(L,t) and given pollution source characteristics c(0,t)=f(t), let us determine the filtration rate v and convective diffusion coefficient D.