Blow up Analysis for Anomalous Granular Gases

Thomas Rey (1)

1 ICJ - Institut Camille Jordan

We investigate in this article the long-time behaviour of the solutions to the energy-dependent, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under statistical description, that dissipates energy during collisions. We assume that the gas is ''anomalous'', in the sense that the energy dissipation increases when the temperature decreases. This allows the gas to cool down in finite time. We study the existence, uniqueness and attractiveness of blow up profiles for this model and the cooling law associated, generalizing the classical Haff's Law for granular gases. To this end, we give some new estimates about the third order moment of the inelastic Boltzmann equation with drift term and we introduce new strongly ''non-linear'' self-similar variables

Mots clés: Inelastic Boltzmann equation; hard spheres; spatially homogeneous; anomalous granular gases; cooling process; Haff's Law; self-similar solution; blow up profile.; blow up profile

Domaines: Equations aux dérivées partielles [math.AP]

Thomas Rey. Blow up Analysis for Anomalous Granular Gases. 2011. ⟨hal-00588970v1⟩