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

[摘要] 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 is an element of (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 (alpha) under bar (1) has been obtained in our previous contribution [6]. We complement here our analysis of such a model by showing that, for some alpha(#) explicit, the self-similar profile is unique for alpha is an element of (0, alpha(#)). (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Boltzmann equation;Ballistic annihilation;Self-similar profile;Uniqueness