Inverse source problem in an advection–dispersion–reaction system: application to water pollution
Résumé
In this paper, we consider the problem of identifying an unknown source F(x, t) = λ(t)δ(x − S) in the following system:
\fl \eqalign{(\partial_t -D\partial_{xx} + V\partial_x +R)u(x,t) =F(x, t),&\qquad 0< x<\ell,\quad 0< t< T\\ (\partial_t -D\partial_{xx} +V\partial_x +R)v(x,t)= Ru(x,t),&\qquad 0< x<\ell,\quad 0< t< T}
from measured data [{v(a, t), ∂xv(a, t)}, {v(b, t), ∂xv(b, t)}] for appropriate points a and b. Assuming that the source F became inactive after the time T*(i.e. λ(t) = 0 for t ≥ T*), we prove an identifiability result and propose an identification method.