Reconstruction of two time independent coefficients in an inverse problem for a phase field system

In this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain Ω⊂RnΩ⊂Rn for the dimension n≤3n≤3 with a single observation on a subdomain ω⋐Ωω⋐Ω and the Sobolev norm of certain partial derivatives of the solutions at a fixed positive time θ∈(0,T)θ∈(0,T) over the whole spatial domain. The proof of these results relies on an appropriate Carleman estimate for the phase field system.