{"paper":{"title":"A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Francis Filbet (IMT), Maxime Herda (ICJ)","submitted_at":"2016-06-03T14:32:55Z","abstract_excerpt":"We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media equations, Fokker-Planck equations for plasma physics or dumbbell models for polymer flows, it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme is built from a discretization of the steady equation and preserves steady-states and natural Lyapunov functionals which provide a satisfying long-time be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01104","kind":"arxiv","version":5},"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"}