第9796回北大MMCセミナー

Abstract: Cahn’s time cone model describes the dependency of the phase transformation frequency upon the nucleation rate and the growth speed, which is important in material science and manufacturing industry.

Especially, the reconstruction of the nucleation rate possesses remarkable significance in some industrial applications. However, the original formulation of Cahn’s model is inconvenient to handle, preventing us from effective simulation of the forward problem and the study of inverse problems. In this talk, we first discuss the reduction of the original model to a class of multiple hyperbolic systems, which enables the development of dramatically fast forward solvers in practical dimensions. Next, within the framework of inverse source problems for hyperbolic-type equations, we investigate the determination of the spatial distribution of the nucleation rate by two kinds of observation data. In case of the final observation, we employ the analytic Fredholm theory to show the generic well-posedness. In case of the partial interior observation, we prove Lipschitz stability on basis of Carleman estimates. For the numerical reconstruction, we develop a universal iterative thresholding algorithm for both observation data.

Extensive numerical experiments demonstrate the efficiency and accuracy of the purposed algorithm.