{"paper":{"title":"Initial trace of solutions of Hamilton-Jacobi parabolic equation with absorption","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":"2014-07-16T19:42:56Z","abstract_excerpt":"Here we study the initial trace problem for the nonnegative solutions of the equation \\[ u\\_{t}-\\Delta u+|\\nabla u|^{q}=0 \\] in $Q\\_{\\Omega,T}=\\Omega\\times\\left( 0,T\\right) ,$ $T\\leqq\\infty,$ where $q>0,$ and $\\Omega=\\mathbb{R}^{N},$ or $\\Omega$ is a smooth bounded domain of $\\mathbb{R}^{N}$ and $u=0$ on $\\partial\\Omega\\times\\left( 0,T\\right) .$ We can define the trace at $t=0$ as a nonnegative Borel measure $(\\mathcal{S} ,u\\_{0}),$ where $S$ is the closed set where it is infinite, and $u\\_{0}$ is a Radon measure on $\\Omega\\backslash\\mathcal{S}.$ We show that the trace is a Radon measure when "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4442","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"}