报告题目 (Title)：An optimal control of a variable-order fractional PDE(变分数阶偏微分方程的优化控制)

报告人 (Speaker)：王宏教授（南卡罗来纳大学）

报告时间 (Time)：2021年11月28日(周日) 8:00

报告地点 (Place)：腾讯会议，会议ID: 914 340 244

邀请人(Inviter)：李常品、蔡敏

主办部门：理学院数学系

报告摘要：Optimal control of fractional diffusion PDEs demonstrates its competitive modeling abilities of challenging phenomena as anomalously diffusive transport and long-range interactions. In applications as bioclogging and oil/gas recovery, the structure of porous materials may evolve in time that leads to variable-order fractional FDEs via the Hurst index of the fractal dimension of the porous materials.

The variable-order optimal control encounters mathematical and numerical issues that are not common in its integer-order and constant-order fractional analogues: (i) The adjoint state equation of the variable-order Caputo time-fractional PDE turns out to be a different and more complex type of variable-order Riemann-Liouville time-fractional PDE. (ii) The coupling of the variable-order fractional state PDE and adjoint state PDE, and the variational inequality reduces the regularity of the solution to the optimal control. (iii) The numerical approximation to fractional optimal control model needs to be analyzed due to the low regularity and coupling of the model. We will prove the wellposedness and regularity of the model and an optimal-order error estimate to its numerical discretization.