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Nonlocal Continuum Limits of p-Laplacian Problems on Graphs

Jalal Fadili author Abderrahim Elmoataz author Imad El Bouchairi author Yosra Hafiene author

Format:Paperback

Publisher:Cambridge University Press

Published:11th May '23

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Nonlocal Continuum Limits of p-Laplacian Problems on Graphs cover

Considers fully discretized p-Laplacian 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.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.

ISBN: 9781009327855

Dimensions: 229mm x 152mm x 7mm

Weight: 91g

75 pages