{"paper":{"title":"Does the fully parabolic quasilinear 1D Keller-Segel system enjoy long-time asymptotics analogous to its parabolic-elliptic simplification?","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Cristian Morales-Rodrigo, Jan Burczak, Tomasz Cie\\'slak","submitted_at":"2011-11-07T13:59:12Z","abstract_excerpt":"We show that the one-dimensional fully parabolic Keller-Segel system with nonlinear diffusion possesses global-in-time solutions, provided the nonlinear diffusion is equal to (1+u)^{-\\alpha}, for \\alpha < 1, independently on the volume of the initial data. We also show that in the critical case, i.e. for \\alpha = 1, the same result holds for initial masses smaller than a prescribed constant. Additionally, we prove existence of initial data for which solution blows up in a finite time for any nonlinear diffusion integrable at infinity. Thus we generalize the known blowup result of parabolic-ell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1580","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"}