报告题目：Determining the nonlinear energy potential in phase-field system

报告人：倪天昊  复旦大学

报告时间：2025年9月12日 下午 15:00-16:00

报告地点：腾讯会议：486-852-074

校内联系人：张剑桥 [email protected]

报告摘要：The phase-field system serves as a crucial nonlinear model in materials science with significant application value in the design of alloys for extreme working conditions. This report primarily focuses on the uniqueness of determining the nonlinear energy potential function in a coupled Cahn-Hilliard and Allen-Cahn phase-field system, theoretically proving that the reconstruction of the energy potential function can be uniquely achieved based solely on concentration field measurements. In the numerical section, a model reduction approach is employed to establish an inversion algorithm for the potential function that relies only on concentration field data at two time points, enabling stable identification of the coefficients in the nonlinear terms.

报告人简介：Dr Tianhao Ni is currently conducting postdoctoral research at the School of Mathematical Sciences, Fudan University, under the supervision of Professor Shuai Lu. He obtained his Ph.D. in Mathematics from Zhejiang University in 2025, where he was advised by Professor Jun Lai. His primary research focuses on the inverse problem theory and numerical computation of nonlinear partial differential equations.

In his academic work, he has established a uniqueness theory for coefficient determination in inverse problems of quasilinear hyperbolic equations based on the Dirichlet-to-Neumann mapping, with related results published in the Journal of Functional Analysis. Furthermore, in his study of inverse problems for phase-field equations, he developed a novel proof methodology utilizing higher-order linearization techniques, achieving unique reconstruction of nonlinear potential functions through single-measurement data, with findings published in Inverse Problems.