{"paper":{"title":"Steady states, global existence and blow-up for fourth-order semilinear parabolic equations of Cahn--Hilliard type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pablo Alvarez-Caudevilla, Victor A. Galaktionov","submitted_at":"2013-11-04T15:02:38Z","abstract_excerpt":"Fourth-order semilinear parabolic equations of the Cahn--Hilliard-type (01) u_t + \\D^2 u = \\g u \\pm \\D (|u|^{p-1}u) in \\Omega \\times \\re_+, are considered in a smooth bounded domain $\\O \\subset \\ren$ with Navier-type boundary conditions on $\\p \\O$, or $\\O = \\ren$, where $p>1$ and $\\g$ are given real parameters. The sign $``+\"$ in the \"diffusion term\" on the right-hand side means the stable case, while $``-\"$ reflects the unstable (blow-up) one, with the simplest, so called limit, canonical model for $\\g=0$, (02) u_t + \\D^2 u= \\pm \\D(|u|^{p-1}u) \\inA. The following three main problems are studi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0723","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"}