SELF-SIMILARITY FOR BALLISTIC AGGREGATION EQUATION

Miguel Escobedo (1) , Stéphane Mischler (2)

1 Departamento de Matemáticas [Bilbao]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider ballistic aggregation equation for gases in which each particle is iden- tified either by its mass and impulsion or by its sole impulsion. For the constant aggregation rate we prove existence of self-similar solutions as well as convergence to the self-similarity for generic solutions. For some classes of mass and/or impulsion dependent rates we are also able to estimate the large time decay of some moments of generic solutions or to build some new classes of self-similar solutions.

Domaines: Equations aux dérivées partielles [math.AP]

Miguel Escobedo, Stéphane Mischler. SELF-SIMILARITY FOR BALLISTIC AGGREGATION EQUATION. Journal of Statistical Physics, 2010, 144, pp.422-458. ⟨hal-00429213⟩