Introduction: big data and partial differential equations
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:...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
Cambridge University Press
2017
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/49501/ |
| _version_ | 1848798012225093632 |
|---|---|
| author | van Gennip, Yves Schönlieb, Carola-Bibiane |
| author_facet | van Gennip, Yves Schönlieb, Carola-Bibiane |
| author_sort | van Gennip, Yves |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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]. |
| first_indexed | 2025-11-14T20:13:00Z |
| format | Article |
| id | nottingham-49501 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:13:00Z |
| publishDate | 2017 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-495012020-05-04T19:25:11Z https://eprints.nottingham.ac.uk/49501/ Introduction: big data and partial differential equations van Gennip, Yves Schönlieb, Carola-Bibiane 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]. Cambridge University Press 2017-12-31 Article PeerReviewed van Gennip, Yves and Schönlieb, Carola-Bibiane (2017) Introduction: big data and partial differential equations. European Journal of Applied Mathematics, 28 (6). pp. 877-885. ISSN 1469-4425 Big data; Partial differential equations; Graphs; Discrete to continuum; Probabilistic domain decomposition https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/introduction-big-data-and-partial-differential-equations/668B59ED2B0541ABE1A8E938D15D0E3C doi:10.1017/S0956792517000304 doi:10.1017/S0956792517000304 |
| spellingShingle | Big data; Partial differential equations; Graphs; Discrete to continuum; Probabilistic domain decomposition van Gennip, Yves Schönlieb, Carola-Bibiane Introduction: big data and partial differential equations |
| title | Introduction: big data and partial differential equations |
| title_full | Introduction: big data and partial differential equations |
| title_fullStr | Introduction: big data and partial differential equations |
| title_full_unstemmed | Introduction: big data and partial differential equations |
| title_short | Introduction: big data and partial differential equations |
| title_sort | introduction: big data and partial differential equations |
| topic | Big data; Partial differential equations; Graphs; Discrete to continuum; Probabilistic domain decomposition |
| url | https://eprints.nottingham.ac.uk/49501/ https://eprints.nottingham.ac.uk/49501/ https://eprints.nottingham.ac.uk/49501/ |