{"paper":{"title":"Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Blake Barker, Kevin Zumbrun, Shantia Yarahmadian, Sidney L. Shaw","submitted_at":"2010-04-12T02:09:52Z","abstract_excerpt":"We generalize the Dogterom-Leibler model for microtubule dynamics [DL] to the case where the rates of elongation as well as the lifetimes of the elongating and shortening phases are a function of GTP-tubulin concentration. We study also the effect of nucleation rate in the form of a damping term which leads to new steady-states. For this model, we study existence and stability of steady states satisfying the boundary conditions at x = 0. Our stability analysis introduces numerical and analytical Evans function computations as a new mathematical tool in the study of microtubule dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1866","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"}