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6-19天元基金几何与随机分析及其应用交叉讲座之66【田小川】

报告题目: Nonlocal models with a finite range of nonlocal interactions
报告人:Dr. Xiaochuan Tian, Applied Physics and Applied Mathematics Department,Columbia University
报告时间:6月19日  10:00
报告地点:1208

摘要: As alternatives to partial differential equations (PDEs), nonlocal continuum models given in integral forms avoid the explicit use of derivatives and allow solutions to exhibit desired singular behavior. We present in this talk nonlocal models of mechanics and diffusion processes characterized by a horizon parameter which measures the range of nonlocal interactions. Considering their close connections to classical local PDE models in the limit when the horizon parameter shrinks to zero and to global fractional PDEs in the limit when the horizon parameter tends to infinity, we present numerical schemes that are robust under the changes of the horizon parameter. We also discuss the coupling of models characterized by different scales of horizon.


  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会