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Article Dans Une Revue Journal of Differential Equations Année : 2013

Existence of self-similar profile for a kinetic annihilation model

Résumé

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 $\alpha \in (0,1)$ or they undergo an elastic collision with probability $1 - \alpha$. For such a model, the number of particles, the linear momentum and the kinetic energy are not conserved. We show that, for $\alpha$ smaller than some explicit threshold value $ \alpha_*$, a self-similar solution exists.
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Dates et versions

hal-00732505 , version 1 (14-09-2012)
hal-00732505 , version 2 (10-10-2014)

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Véronique Bagland, Bertrand Lods. Existence of self-similar profile for a kinetic annihilation model. Journal of Differential Equations, 2013, 254 (7), pp.3023-3080. ⟨10.1016/j.jde.2013.01.020⟩. ⟨hal-00732505v2⟩
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