Inverse coefficient problems for a transport equation by local Carleman estimate,

We consider the transport equation $ppp_tu(x,t) + (H(x)cdot abla u(x,t)) + p(x)u(x,t) = 0$ in $OOO imes (0,T)$ where $OOO subset R^n$ is a bounded domain, and discuss two inverse problems which consist of determining a vector-valued function $H(x)$ or a real-valued function $p(x)$ by initial values and data on a subboundary of $OOO$. Our results are conditional stability of H"older type in a subdomain $D$ provided that the outward normal component of $H(x)$ is positive on $ppp D cap pppOOO$. The proofs are based on a Carleman estimate where the weight function depends on $H$.