讲座题目：On mathematical models by (variable-order) time-fractional diffusion equations 主讲人：王宏 教授 主持人：羊丹平 教授 开始时间：2019-05-10 13:30:00 结束时间：2019-05-10 14:30:00 讲座地址：闵行数学楼401报告厅 主办单位：数学科学学院
报告人简介： 王宏，美国南卡罗来纳大学数学系终身教授，分别于1982年和1984年获山东大学数学学士学位和计算数学硕士学位，1992年获美国怀俄明大学数学博士学位。主要从事油气田勘探开发、环境污染的预测与治理和二氧化碳埋存等领域的数学模型、数值模拟与大规模科学计算的理论及应用方面的研究；迄今为止已在美国工业与应用数学会的多种期刊（SIAM J Numer. Anal.、 SIAM Sci. Comput.）、计算物理杂志（J Comput Phys）、Numer. Methods PDEs和英国IMA J. Numer. Anal.等国际权威学术杂志发表论文百余篇。王宏教授还是Numer. Methods PDEs、Computing and Visualization in Sciences、Int J. Numer. Anal. Modeling等国际知名杂志的编委。王宏教授的研究得到了美国国家自然科学基金会、挪威自然科学基金会、南卡州以及世界排名前列的石油公司等的多项基金资助。 报告内容： Recently, Stynes et al proved that time-fractional diffusion equations (tFDEs) generate solutions with singularity near the initial time t=0, which makes the error estimates in the literature that were proved under full regularity assumptions of the true solutions inappropriate. From a modeling point of view, the singularities of the solutions to tFDEs at t=0 do not seem physically relevant to the diffusive transport the tFDEs model. The fundamental reason lies between the incompatibility between the nonlocality of tFDEs and the locality of the initial condition. To eliminate the incompatibility, we propose a modified tFDE model in which the fractional order will vary near the time t=0, which naturally leads to variable-order tFDEs. We will also show that variable-order tFDEs occur naturally in applications. Finally, we briefly discuss the mathematical difficulties in the analysis of variable-order tFDEs, since many widely used Laplace transform based techniques do not apply here. |
