{"paper":{"title":"Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Mohamed Majdoub, Sarah Otsmane, Slim Tayachi","submitted_at":"2016-06-23T14:23:38Z","abstract_excerpt":"In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $\\partial_{t} u+ \\Delta^2 u=f(u),\\;t>0,\\;x\\in\\R^N,$ with $f(u)\\sim \\mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential nonlinearity $f$ such that $f(u)\\sim u^m$ as $u\\to 0,$ $m$ integer and $N(m-1)/4\\geq 2$, we show that the solution is global. Moreover, we obtain a decay estimates for large time for the nonlinear biharmonic heat equation as well as for the nonlinear heat equation. Our results extend to the nonlinear polyharmonic heat equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07320","kind":"arxiv","version":3},"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"}