{"paper":{"title":"Continuity of attractors for a family of $C^1$ perturbations of the square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ant\\^onio L. Pereira, Marcone C. Pereira, Pricila S. Barbosa","submitted_at":"2016-03-19T15:26:27Z","abstract_excerpt":"We consider here the family of semilinear parabolic problems \\begin{equation*} \\begin{array}{rcl} \\left\\{ \\begin{array}{rcl} u_t(x,t)&=&\\Delta u(x,t) -au(x,t) + f(u(x,t)) ,\\,\\,\\ x \\in \\Omega_\\epsilon \\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\\,t>0\\,, \\\\ \\displaystyle\\frac{\\partial u}{\\partial N}(x,t)&=&g(u(x,t)), \\,\\, x \\in \\partial\\Omega_\\epsilon \\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\\,t>0\\,, \\end{array} \\right. \\end{array} \\end{equation*} where $ {\\Omega} $ is the unit square, $\\Omega_{\\epsilon}=h_{\\epsilon}(\\Omega)$ and $h_{\\epsilon}$ is a family of diffeomorphisms converging to the identity in the $C^1$-norm. We show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06104","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"}