{"paper":{"title":"Instantaneous shrinking and single point extinction for viscous Hamilton-Jacobi equations with fast diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christian Stinner, Philippe Lauren\\c{c}ot (IMT), Razvan Gabriel Iagar (ICMAT)","submitted_at":"2015-10-02T06:31:29Z","abstract_excerpt":"For a large class of non-negative initial data, the solutions to the quasilinear viscous Hamilton-Jacobi equation $\\partial\\_t u-\\Delta\\_p u+|\\nabla u|^q=0$ in $(0,\\infty)\\times\\real^N$ are known to vanish identically after a finite time when $2N/(N+1) \\textless{} p \\leq 2$ and $q\\in(0,p-1)$. Further properties of this extinction phenomenon are established herein: \\emph{instantaneous shrinking} of the support is shown to take place if the initial condition $u\\_0$ decays sufficiently rapidly as $|x|\\to\\infty$, that is, for each $t \\textgreater{} 0$, the positivity set of $u(t)$ is a bounded sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00500","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"}