Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data

To compute the spatially distributed dielectric constant from backscattering computationally simulated ane experimentally collected data, we study a coefficient inverse problem for 1D hyperbolic equation. solve this problem, establish new version of Carleman estimate and then employ to construct cost functional, which is strictly convex on bounded set an arbitrary diameter in Hilbert space. The strict convexity property rigorously proved. This result called convexification theorem it central analytical paper. Minimizing functional by gradient descent method, obtain desired numerical solution problems. We prove that method generates sequence converging minimizer starting point set. also confirming converges true as noise measured data regularization parameter tend zero. Unlike methods, are based optimization, our globally sense delivers good approximation exact without requiring initial guess. Results studies both presented.