Introduction: Big data and partial differential equations
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Authors
Van Gennip, Y
Schönlieb, CB
Publication Date
2017-12-01Journal Title
European Journal of Applied Mathematics
ISSN
0956-7925
Publisher
Cambridge University Press (CUP)
Volume
28
Issue
6
Pages
877-885
Type
Article
This Version
AM
Metadata
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Van Gennip, Y., & Schönlieb, C. (2017). Introduction: Big data and partial differential equations. European Journal of Applied Mathematics, 28 (6), 877-885. https://doi.org/10.1017/S0956792517000304
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].
Sponsorship
Engineering and Physical Sciences Research Council (EP/N014588/1)
Engineering and Physical Sciences Research Council (EP/M00483X/1)
Engineering and Physical Sciences Research Council (EP/J009539/1)
Alan Turing Institute (unknown)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)
Identifiers
External DOI: https://doi.org/10.1017/S0956792517000304
This record's URL: https://www.repository.cam.ac.uk/handle/1810/292775
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