|
Applied Math Seminar
High Velocity Tails for Energy Dissipative Boltzmann Equations
|
|
We present energy dissipative Boltzmann equations modeling statistical kinetics of inelastic or mixtures of elastic interactions. These are models for rapid granular flows (inelastic case) or chemical reactions (elastic mixtures). We discuss issues of existence, uniqueness and stability of selfsimilar solutions for variable hard sphere models. We show selfsimilar solutions deviate from statistical equilibrium solutions (Maxwellian distributions) in steady and transient regimes. In addition, we point out the differences in terms of high energy tail behavior between Maxwell molecules and variable hard spheres models for self-similar energy dissipative collisional flows. The former exhibit decay given by a power law, while the latter remains exponential with slower decay rate than Gaussians tails. Our analysis extend to forces equations such as randomly heated granular flows and inelastic shear flow. |