Simultaneously identifying the thermal conductivity and radiative coefficient in heat equation from Dirichlet and Neumann boundary measured outputs

This paper deals with an inverse coefficient problem of simultaneously identifying the thermal conductivity k(x) and radiative coefficient q(x) in the 1D heat equation u(t) = (k(x)u(x))(x) - q(x)u from the most available Dirichlet and Neumann boundary measured outputs. The Neumann-to-Dirichlet and Neumann-to-Neumann operators Phi[k, q](t) := u(l, t; k, q), Psi[k, q](t) := -k(0)u(x)(0, t; k, q) are introduced, and main properties of these operators are derived. Then the Tikhonov functional