Self-similar solutions with fat tails for a coagulation equation with nonlocal drift

Michael Herrmann; Philippe Laurençot; Barbara Niethammer

doi:10.1016/j.crma.2009.05.006

Partial Differential Equations

Self-similar solutions with fat tails for a coagulation equation with nonlocal drift
[Solutions auto-similaires à décroissance lente pour une équation de coagulation avec transport non local]

Présenté par : Haïm Brezis

Michael Herrmann ¹ ; Philippe Laurençot ² ; Barbara Niethammer ¹

¹ Oxford Centre for Nonlinear PDE, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United Kingdom
² Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS UMR 5219, 118, route de Narbonne, F-31062 Toulouse cedex 9, France

Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 909-914.

Résumé
Abstract

L'existence de solutions auto-similaires préservant le volume total est établie pour une équation de coagulation incluant un terme de transport non local. Bien que cette équation admette des profils auto-similaires décroissant exponentiellement à l'infini, des profils auto-similaires avec une décroissance algébrique à l'infini sont construits lorsque le volume total est suffisamment petit.

We investigate the existence of self-similar solutions for a coagulation equation with nonlocal drift. In addition to explicitly given exponentially decaying solutions we establish the existence of self-similar profiles with algebraic decay.

Reçu le : 2009-01-26
Accepté le : 2009-05-11
Publié le : 2009-06-21

DOI : 10.1016/j.crma.2009.05.006

Affiliations des auteurs :

Michael Herrmann ¹ ; Philippe Laurençot ² ; Barbara Niethammer ¹

¹ Oxford Centre for Nonlinear PDE, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United Kingdom
² Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS UMR 5219, 118, route de Narbonne, F-31062 Toulouse cedex 9, France

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     author = {Michael Herrmann and Philippe Lauren\c{c}ot and Barbara Niethammer},
     title = {Self-similar solutions with fat tails for a coagulation equation with nonlocal drift},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {909--914},
     publisher = {Elsevier},
     volume = {347},
     number = {15-16},
     year = {2009},
     doi = {10.1016/j.crma.2009.05.006},
     language = {en},
}

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Michael Herrmann; Philippe Laurençot; Barbara Niethammer. Self-similar solutions with fat tails for a coagulation equation with nonlocal drift. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 909-914. doi : 10.1016/j.crma.2009.05.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.05.006/

Bibliographie
Cité par

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