Analysis and Applications of Nonlocal Models

Explore the fascinating world of nonlocal models in this 44-minute SIAM Invited Address given by Qiang Du from Columbia University at the Virtual Joint Mathematics Meetings. Delve into the comparison between local and nonlocal approaches, and discover the growing interest in nonlocal models in recent decades. Learn about nonlocal vector calculus for finite-range interactions and examine various examples of nonlocal operators. Investigate the opportunities and challenges presented by nonlocal modeling, including interactions with a finite horizon parameter. Gain insights into robust numerical discretization techniques and solutions for nonlocal models. The lecture concludes with references and further discussions on this intriguing mathematical topic.

Intro
Local vs Nonlocal
Nonlocal models: surging interests in recent decades
Nonlocal vector calculus for interactions of finite range
Examples of Nonlocal Operators
Nonlocal Operators and Nonlocal Vector Calculus
Nonlocal modeling opportunities and challenges
Nonlocal interactions with a finite horizon parameter 8
Robust numerical discretization of nonlocal models
Numerical solution of nonlocal models
References
More discussions on nonlocal models