{"paper":{"title":"Local null controllability for degenerate parabolic equations with nonlocal term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan L\\'imaco, Luiz Viana, Reginaldo Demarque","submitted_at":"2016-12-28T00:03:52Z","abstract_excerpt":"We establish a local null controllability result for following the nonlinear parabolic equation: $$u_t-\\left(b\\left(x,\\int_0^1u \\ \\right)u_x \\right)_x+f(t,x,u)=h\\chi_\\omega,\\ (t,x)\\in (0,T)\\times (0,1) $$ where $b(x,r)=\\ell(r)a(x)$ is a function with separated variables that defines an operator which degenerates at $x=0$ and has a nonlocal term. Our approach relies on an application of Liusternik's inverse mapping theorem that demands the proof of a suitable Carleman estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08774","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"}