The phase-field system is a nonlinear model that has significant applications in the field of materials science. In this talk, we are concerned with the uniqueness of determining the nonlinear energy potential in a phase-field system consisted of Cahn-Hilliard and Allen-Cahn equations. This system finds widespread applications in the development of alloys engineered to withstand extreme temperatures and pressures. The goal is to reconstruct the nonlinear energy potential through the measurements of concentration fields. We establish the local well-posedness of the phase-field system based on the implicit function theorem in Banach spaces. Both of the uniqueness results for recovering time-independent and time-dependent energy potential functions are provided through the higher order linearization technique. We also propose a numerical inverse method called dual-time phase-field inversion (DTPFI) in the end.

报告人简介：赖俊，浙江大学数学科学学院长聘教授，主要研究声波，电磁波及弹性波方程的散射与反散射问题，在数学知名杂志ACHA，SIAM系列，Inverse Problems等发表文章多篇。主持基金委面上、国家重点研发计划等项目，并参与基金委重大研究计划集成项目、基金委创新群体等研究。2023年第十三届全国计算数学年会和2025年国际应用反问题会议大会特邀报告人，2024 年获中国工业与应用数学学会”应用数学青年科技奖“，2025年入选教育部长江特聘教授。