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Nonlocal Continuum Limits of p-Laplacian Problems on Graphs.
・ISBN 978-1-009-32785-5 paper GB£ 18.00
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電子版あり 大学・学術機関向け電子ブック(eBook)ISBN 978-1-009-32786-2
| 著者・編者 | El Bouchairi, Imad / Fadili, Jalal / Hafiene, Yosra / Elmoataz, Abderrahim, |
|---|---|
| シリーズ | Elements in Non-local Data Interactions: Foundations and Applications |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2023 |
| ページ数 | 75 pp. |
| 言語 | ENG |
| ニュース番号 | <M25-14097> |
解説
In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs. The motivation of nonlocal continuum limits comes from the quest of understanding collective dynamics in large ensembles of interacting particles, which is a fundamental problem in nonlinear science, with applications ranging from biology to physics, chemistry and computer science. Using the theory of graphons, the authors give a unified treatment of all the above problems and establish the continuum limit for each of them together with non-asymptotic convergence rates. They also describe an algorithmic framework based proximal splitting to solve these discrete problems on graphs.