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

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 α ∈ (0, 1) or they undergo an elastic collision with probability 1 − α. The existence of a self-similar profile for α smaller than an explicit threshold value α1 has been obtained in our previous contribution [6]. We complement here our analysis of such a model by showing that, for some α explicit, the self-similar profile is unique for α ∈ (0, α).