Reconstruction of two constant coefficients in linear anisotropic diffusion model

Abstract

Let be a complex Hilbert space and and be nonnegative and selfadjoint operators. We study the inverse problem consisting in the identification of the function and two constants α, (diffusion coefficients) that fulfill the initial-value problemu′(t)+αAu(t)+βBu(t)=0,t∈(0,T),u(0)=x,and the additional conditions〈Au(T),u(T)〉=φand〈Bu(T),u(T)〉=ψ.Under suitable assumptions on the operators A and B, and on the data and , we shall construct a solution and prove its uniqueness and continuous dependence on the data. Applications are considered.