Uniqueness and stability of an inverse problem for a phase field model using data from one component

• A Carleman estimate for the parabolic–hyperbolic phase field system is proved.
• Lipschitz stability and uniqueness for a coefficient inverse problem for this phase field system using data from one component are established.
• Lipschitz stability provides theoretical support for numerical methods.

We study an inverse problem of determining a spatial varying coefficient in a parabolic–hyperbolic phase field model with the following observation data of only one component: the order parameter in a subdomain ωω satisfying ∂ω⊃∂Ω∂ω⊃∂Ω along a sufficiently large time interval and at a suitable time over the whole spatial domain. Based on a Carleman estimate for the parabolic–hyperbolic phase field system, we prove the Lipschitz stability and uniqueness for this inverse problem.