{"paper":{"title":"Admissible initial growth for diffusion equations with weakly superlinear absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrey Shishkov (IAMM), Laurent V\\'eron (LMPT)","submitted_at":"2015-03-30T04:59:16Z","abstract_excerpt":"We study the admissible growth at infinity of initial data of positive solutions of $\\prt\\_t u-\\Gd u+f(u)=0$ in $\\BBR\\_+\\ti\\BBR^N$ when $f(u)$ is a continuous  function, {\\it mildly} superlinear at infinity, the model case being $f(u)=u\\ln^\\ga (1+u)$ with $1\\textless{}\\ga\\textless{}2$. We prove in particular that if the growth of the initial data at infinity  is too strong, there is no more diffusion and the corresponding solution satisfies the ODE problem $\\prt\\_t \\gf+f(\\gf)=0$ on $\\BBR\\_+$ with $\\gf(0)=\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08532","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"}