{"paper":{"title":"Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"V.A. Galaktionov","submitted_at":"2009-01-27T18:29:49Z","abstract_excerpt":"Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type\n  $$ u_t= -\\Delta^2 u + |u|^{p-1} u \\quad {in} \\quad \\ren \\times (0,T), p>1, \\quad \\lim_{t \\to T^-}\\sup_{x \\in \\ren} |u(x,t)|= +\\iy, $$ are discussed. For the semilinear heat equation $u_t= \\Delta u+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4307","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"}