Uniqueness of the self-similar profile for a kinetic annihilation model - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2015

Uniqueness of the self-similar profile for a kinetic annihilation model

Résumé

We prove the uniqueness of the self-similar profile solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability $\alpha \in (0,1)$ or they undergo an elastic collision with probability $1-\alpha$. The existence of a self-similar profile for $\alpha$ smaller than an explicit threshold value $\underline{\alpha}_1$ has been obtained in our previous contribution (J. Differential Equations, 254, 3023--3080, 2013). . We complement here our analysis of such a model by showing that, for some $\alpha^{\sharp} $ explicit, the self-similar profile is unique for $\alpha \in (0,\alpha^{\sharp})$.
Fichier principal
Vignette du fichier
VB-BL-JDE.pdf (448.42 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01015795 , version 1 (27-06-2014)

Identifiants

Citer

Véronique Bagland, Bertrand Lods. Uniqueness of the self-similar profile for a kinetic annihilation model. Journal of Differential Equations, 2015, 259 (12), pp.7012-7059. ⟨10.1016/j.jde.2015.08.011⟩. ⟨hal-01015795⟩
201 Consultations
224 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More