Identifications of parameters in ill-posed linear parabolic equations Original Research Article

In this paper, we study the identification of conductivities q in linear parabolic equation ∂y/∂t−∇·(q∇y)=f in Ω×(0,T) with boundary condition y(x,t)=0 on ∂Ω×(0,T) and without initial data, where the observations are taken in an open subset of Ω. We obtain the existence and introduce an approximation process for the identification problem.