{"paper":{"title":"Classification of extinction profiles for a one-dimensional diffusive hamilton-jacobi equation with critical absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Philippe Lauren\\c{c}ot (IMT), Razvan Iagar (ICMAT)","submitted_at":"2016-06-01T08:43:25Z","abstract_excerpt":"A classification of the behavior of the solutions $f(\\cdot,a)$ to the ordinary differential equation $(|f'|^{p-2} f')' + f - |f'|^{p-1} = 0$ in $(0,\\infty)$ with initial condition $f(0,a)=a$ and $f'(0,a)=0$ is provided, according to the value of the parameter $a>0$, the exponent $p$ ranging in $(1,2)$. There is a threshold value $a_*$ which separates different behaviors of $f(\\cdot,a)$: if $a>a_*$ then $f(\\cdot,a)$ vanishes at least once in $(0,\\infty)$ and takes negative values while $f(\\cdot,a)$ is positive in $(0,\\infty)$ and decays algebraically to zero as $r\\to\\infty$ if $a\\in (0,a_*)$. A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00172","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"}