{"paper":{"title":"Exponential trend to equilibrium for the inelastic Boltzmann equationdriven by a particle bath","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bertrand Lods, Jos\\'e Alfredo Ca\\~nizo","submitted_at":"2015-07-02T06:45:48Z","abstract_excerpt":"We consider the spatially homogeneous Boltzmann equation for  inelastic hard spheres (with constant restitution coefficient  $\\alpha \\in (0,1)$) under the thermalization induced by a host  medium with a fixed Maxwellian distribution. We prove that the  solution to the associated initial-value problem converges  exponentially fast towards the unique equilibrium solution. The  proof combines a careful spectral analysis of the linearised  semigroup as well as entropy estimates. The trend towards  equilibrium holds in the weakly inelastic regime in which $\\alpha$  is close to $1$, and the rate of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00440","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}