{"paper":{"title":"Isolated initial singularities for the viscous Hamilton-Jacobi equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Nguyen Anh Dao (LMPT)","submitted_at":"2012-01-09T14:18:18Z","abstract_excerpt":"Here we study the nonnegative solutions of the viscous Hamilton-Jacobi equation [u_{t}-\\Delta u+|\\nabla u|^{q}=0] in $Q_{\\Omega,T}=\\Omega\\times(0,T),$ where $q>1,T\\in(0,\\infty] ,$ and $\\Omega$ is a smooth bounded domain of $\\mathbb{R}% ^{N}$ containing $0,$ or $\\Omega=\\mathbb{R}^{N}.$ We consider solutions with a possible singularity at point $(x,t)=(0,0).$ We show that if $q\\geq q_{\\ast}=(N+2)/(N+1)$ the singularity is removable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1774","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"}