{"paper":{"title":"Global analytic solutions of the semiconductor Boltzmann-Dirac-Benney equation with relaxation time approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcel Braukhoff","submitted_at":"2018-03-01T14:35:43Z","abstract_excerpt":"The global existence of a solution of the semiconductor Boltzmann-Dirac-Benney equation \\[ \\partial_t f + \\nabla\\epsilon(p)\\cdot\\nabla_x f - \\nabla \\rho_f(x,t)\\cdot\\nabla_p f = \\frac{\\mathcal F_\\lambda(p)-f}\\tau, \\quad x\\in\\mathbb{R}^d,\\ p\\in B, \\ t>0 \\] is shown for small $\\tau>0$ assuming that the initial data are analytic and sufficiently close to $\\mathcal F_\\lambda$. This system contains an interaction potential $\\rho_f(x,t):=\\int_{B}f(x,p,t)dp$ being significantly more singular than the Coulomb potential, which causes major structural difficulties in the analysis. The semiconductor Boltz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00379","kind":"arxiv","version":1},"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"}