Tanaka Theorem for Inelastic Maxwell Models

François Bolley (1) , José Antonio Carrillo (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UAB - Departament de Matemàtiques [Barcelona]

We show that the Euclidean Wasserstein distance is contractive for inelastic homogeneous Boltzmann kinetic equations in the Maxwellian approximation and its associated Kac-like caricature. This property is as a generalization of the Tanaka theorem to inelastic interactions. Consequences are drawn on the asymptotic behavior of solutions in terms only of the Euclidean Wasserstein distance.

Domaines: Equations aux dérivées partielles [math.AP]

François Bolley, José Antonio Carrillo. Tanaka Theorem for Inelastic Maxwell Models. Communications in Mathematical Physics, 2007, 276 (2), pp.287--314. ⟨hal-00022846⟩