Introduction: big data and partial differential equations

van Gennip, Yves; Sch�nlieb, Carola-Bibiane

Abstract

Partial differential equations (PDEs) are expressions involving an unknown function in many independent variables and their partial derivatives up to a certain order. Since PDEs express continuous change, they have long been used to formulate a myriad of dynamical physical and biological phenomena: heat flow, optics, electrostatics and -dynamics, elasticity, fluid flow and many more. Many of these PDEs can be derived in a variational way, i.e. via minimization of an ‘energy’ functional. In this globalised and technologically advanced age, PDEs are also extensively used for modelling social situations (e.g. models for opinion formation, mathematical finance, crowd motion) and tasks in engineering (such as models for semiconductors, networks, and signal and image processing tasks). In particular, in recent years, there has been increasing interest from applied analysts in applying the models and techniques from variational methods and PDEs to tackle problems in data science. This issue of the European Journal of Applied Mathematics highlights some recent developments in this young and growing area. It gives a taste of endeavours in this realm in two exemplary contributions on PDEs on graphs [1, 2] and one on probabilistic domain decomposition for numerically solving large-scale PDEs [3].

Citation

van Gennip, Y., & Schönlieb, C. (2017). Introduction: big data and partial differential equations. European Journal of Applied Mathematics, 28(6), https://doi.org/10.1017/S0956792517000304

• Journal Article Type: Article
• Acceptance Date: Sep 22, 2017
• Online Publication Date: Nov 7, 2017
• Publication Date: Dec 31, 2017
• Deposit Date: Feb 6, 2018
• Publicly Available Date: Feb 6, 2018
• Journal: European Journal of Applied Mathematics
• Print ISSN: 0956-7925
• Electronic ISSN: 1469-4425
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 6
• DOI: https://doi.org/10.1017/S0956792517000304
• Keywords: Big data; Partial differential equations; Graphs; Discrete to continuum; Probabilistic domain decomposition
• Public URL: https://nottingham-repository.worktribe.com/output/902794
• Publisher URL: https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/introduction-big-data-and-partial-differential-equations/668B59ED2B0541ABE1A8E938D15D0E3C