{"paper":{"title":"Construction of a stable blowup solution with a prescribed behavior for a non-scaling invariant semilinear heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"G.K. Duong, H. Zaag, V.T. Nguyen","submitted_at":"2017-04-27T14:05:13Z","abstract_excerpt":"We consider the semilinear heat equation \\begin{eqnarray*} \\partial_t u = \\Delta u + |u|^{p-1} u \\ln ^{\\alpha}( u^2 +2), \\end{eqnarray*} in the whole space $\\mathbb{R}^n$, where $p > 1$ and $ \\alpha \\in \\mathbb{R}$. Unlike the standard case $\\alpha = 0$, this equation is not scaling invariant. We construct for this equation a solution which blows up in finite time $T$ only at one blowup point $a$, according to the following asymptotic dynamics: \\begin{eqnarray*} u(x,t) \\sim \\psi(t) \\left(1 + \\frac{(p-1)|x-a|^2}{4p(T -t)|\\ln(T -t)|} \\right)^{-\\frac{1}{p-1}} \\text{ as } t \\to T, \\end{eqnarray*} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08580","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"}