题目：Fractional Partial Differential Equations: Modeling, Numerical Simulation, and Analysis
报告人：Hong Wang （University of South Carolina and Shandong University）
Fractional partial differential equations (FPDEs) and related nonlocal models are emerging as a powerful tool for modeling challenging multiscale phenomena including overlapping microscopic and macroscopic scales, anomalous transport, and long range time memory or spatial interactions. Compared to integer-order PDEs, the fractional order of the derivatives in FPDEs may be a function of space and time or even a distribution, opening up great opportunities for modeling and simulation of multiphysics phenomena.
The main reasons that these models have not been used extensively so far is that they are quite expensive to solve numerically as they typically generate dense linear algebraic systems due to the nonlocality of fractional differential operators. Furthermore, these models present mathematical and numerical difficulties which were not encountered in the context of integer-order PDEs. We will discuss modeling, numerical and mathematical issues of nonlocal models in this talk.
English
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