I will discuss about sub-diffusion equations with a Clarke subdifferential boundary condition. Such problems model particle transport governed by anomalous diffusion in media with semipermeable boundaries. The weak formulation of the model problem leads to a time-fractional parabolic hemivariational inequality. We first discuss an abstract hemivariational inclusion problem and establish its unique solvability using the Rothe method. Furthermore, we propose and analyze a full discretization of the abstract problem. The obtained results are then applied to prove the convergence of numerical solutions for the model problem. Under appropriate regularity assumptions, we derive an optimal-order error estimate for the numerical method. Finally, we present numerical examples to support the theoretical findings.

许传炬, 厦门大学数学科学学院教授、博士生导师, 闽江学者特聘教授。他于1982年本科毕业于厦门大学数学系, 后赴法国留学, 获巴黎南大学计算数学硕士学位(1989年)和巴黎第六大学理学博士学位(1993年)。2000年起任厦门大学教授, 2008年受聘为闽江特聘教授。其研究方向涵盖偏微分方程数值解、计算流体力学、分数阶偏微分方程高效算法等领域, 发表国际期刊论文40余篇, 主持或参与国家级科研项目20多项 。他长期担任国际学术期刊编委, 培养博士及硕士研究生30余名, 并在国内外多所高校进行学术交流与科普讲座。