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| We consider a modified Boltzmann equation describing probabilistic ballistic annihilation in a spatially homogeneous setting. 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. Physicists expect that any solution to the Boltzmann equation for ballistic annihilation should approach for large times a self-similar solution. We shall investigate here the existence of such self-similar solutions. |
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