2012/09/15 by Véronique Bagland, Bagland, Véronique, Bertrand Lods +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Particle Dynamics in Fluid Flows #Theoretical and Computational Physics #math.AP
paper · pdf · doi:10.48550/arxiv.1209.3379
This new version supersedes and replaces the previous one. We found a mistake in the previous (and published) version of the manuscript and explained how to fix it in "Erratum to "Existence of self-similar profile for a kinetic annihilation model" [J. Differential Equations 254 (7) (2013) 3023-3080]. J. Differential Equations 257 (2014), no. 8, 3071-3074." This version provides a complete and corrected version of the previous manuscript
openalex publication_date 2012/09/15 · arxiv created 2014/10/10 · arxiv updated 2014/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show the existence of a self-similar 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 α∈ (0,1) or they undergo an elastic collision with probability 1 - α. For such a model, the number of particles, the linear momentum and the kinetic energy are not conserved. We show that, for α smaller than some explicit threshold value α_*, a self-similar solution exists.