no. 15-16
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

Herrmann, Michael1 ; Laurençot, Philippe2 ; Niethammer, Barbara1
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, Tome 347 (2009) no. 15-16, pp. 909-914.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.05.006
Herrmann, Michael 1 ; Laurençot, Philippe 2 ; Niethammer, Barbara 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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Herrmann, Michael; Laurençot, Philippe; Niethammer, Barbara. Self-similar solutions with fat tails for a coagulation equation with nonlocal drift. Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 909-914. doi : 10.1016/j.crma.2009.05.006. http://www.numdam.org/articles/10.1016/j.crma.2009.05.006/

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