Inverse coefficient problems for a transport equation by local Carleman estimate

We consider the transport equation ∂tu(x,t)+(H(x) - ∇u(x,t))+p(x)u(x,t)=0 in Ω ×(0,t) where Ω ⊂ ℝn is a bounded domain, and discuss two inverse problems which consist of determining a vector-valued function p(x) or a real-valued function Ω by initial values and data on a subboundary of Ω. Our results are conditional stability of Hölder type in a subdomain D provided that the outward normal component of H(x) is positive on ∂D∩∂Ω. The proofs are based on a Carleman estimate where the weight function depends on H. © 2019 IOP Publishing Ltd.