Convergence to self-similarity for ballistic annihilation dynamics. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2020

Convergence to self-similarity for ballistic annihilation dynamics.

Résumé

We consider the spatially homogeneous Boltzmann equation for ballistic annihilation in dimension d \geq 2. Such model describes a system of ballistic hard spheres that, at the moment of interaction, either annihilate with probability α ∈ (0, 1) or collide elastically with probability 1 − α. Such equation is highly dissipative in the sense that all observables, hence solutions, vanish as time progresses. Following a contribution , by two of the authors, considering well posedness of the steady self-similar profile in the regime of small annihilation rate α ≪ 1, we prove here that such self-similar profile is the intermediate asymptotic attractor to the annihilation dynamics with explicit universal algebraic rate. This settles the issue about universality of the annihilation rate for this model brought in the applied literature.
Fichier principal
Vignette du fichier
A-B-L-Stability-new_3.pdf (788.65 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01767611 , version 1 (16-04-2018)
hal-01767611 , version 2 (19-04-2018)
hal-01767611 , version 3 (25-02-2019)

Licence

Copyright (Tous droits réservés)

Identifiants

Citer

Ricardo J. Alonso, Véronique Bagland, Bertrand Lods. Convergence to self-similarity for ballistic annihilation dynamics.. Journal de Mathématiques Pures et Appliquées, 2020, 138, pp.88-163. ⟨10.1016/j.matpur.2019.09.008⟩. ⟨hal-01767611v3⟩
335 Consultations
185 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More