Conditional Stability In Determining The Highest-order Coefficient In A Half-order Time Fractional Diffusion Equation By A Carleman Estimate

In this thesis, we consider an inverse coefficient problem related to the following frac-tional diffusion equation:Our inverse problem is to determine coefficient p(x) by observation data u(.,t0),t0 ∈ (0,T) and some lateral boundary observation data.We prove a uniqueness and Lipschitz conditional stability for the inverse problem.The key to prove the result is deriving some suitable Carleman estimates. However, it is extremely difficult to prove a Carleman estimate for the operator [(?)1/2 - q2(?)x2). Hence, we first prove a suitable Carleman estimates for the operator ((?9t - q2(?)x4).Then, by using this kind of Carleman estimate, we obtain a uniqueness and Lipschit2 conditional stability for the original inverse problem.