INVERSE PROBLEMS FOR A HALF-ORDER TIME-FRACTIONAL DIFFUSION EQUATION IN ARBITRARY DIMENSION BY CARLEMAN ESTIMATES

We consider a half-order time-fractional diffusion equation in arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some additional assumptions. We establish the stability estimate of Lipschitz type in the inverse problems and the proofs are based on the BukhgeimKlibanov method by using Carleman estimates.

Automated summary

In this study, a half-order time-fractional diffusion equation in arbitrary dimension is considered, and inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time are investigated under some additional assumptions. The stability estimate of Lipschitz type in the inverse problems is established, with proofs based on the BukhgeimKlibanov method using Carleman estimates.