Variable-order Time-Fractional PDEs: modeling, analysis and discretization

摘 要：

Integer-order diffusion PDEs were derived under the assumptions that the underlying particle movements have (i) a mean free path and (ii) a mean waiting time, which hold for the diffusive transport of solutes in homogeneous aquifers when the solute plumes were observed to have Gaussian type symmetric and exponentially decaying tails. However, field tests showed that the diffusive transport of solutes in heterogeneous aquifers often exhibit highly skewed power-law decaying tails. This is because the Gaussian nature of the solutions to integer-order diffusion PDEs makes them hardly catch the highly skewed power-law decaying behavior of the solute transport in heterogeneous media.

Fractional diffusion PDEs were derived assuming their solutions have power-law decaying tails, and so accurately model diffusive transport in heterogeneous aquifers. However, (constant-order) fractional PDEs introduce new modeling, computational and mathematical issues that are not common in the context of integer-order PDEs, partly because they do not handle the transition between local dynamics and nonlocal dynamics. Variable-order fractional PDEs naturally resolve these issues and provide better modeling capabilities to more complex problems. In this talk we will go over these issues and report recent progresses in the field.

报告人：

王宏，美国南卡罗莱纳大学终身教授，杰出数值分析和科学计算专家。王宏教授在数值分析与科学计算、多孔介质渗流力学计算等研究领域取得了许多创造性成果，在计算和应用数学顶级期刊SIAM J. Numer. Anal., SIAM J. Sci. Comput., J. Comput. Phys.等发表文章100余篇。

时  间：2020年11月11日   周三上午8:30-10:00

腾讯会议：417 6381 8666

欢迎广大师生参加！

数学科学学院

2020年11月9日