{"paper":{"title":"Profile for the imaginary part of a blowup solution for a complex-valued seminar heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giao Ky Duong","submitted_at":"2017-12-19T20:02:40Z","abstract_excerpt":"In this paper, we consider the following complex-valued semilinear heat equation \\begin{eqnarray*} \\partial_t u = \\Delta u + u^p, u \\in \\mathbb{C}, \\end{eqnarray*} in the whole space $\\mathbb{R}^n$, where $ p \\in \\mathbb{N}, p \\geq 2$. We aim at constructing for this equation a complex solution $u = u_1 + i u_2$, which blows up in finite time $T$ and only at one blowup point $a$, with the following estimates for the final profile \\begin{eqnarray*} u(x,T) &\\sim & \\left[ \\frac{(p-1)^2 |x-a|^2}{ 8 p |\\ln|x-a||}\\right]^{-\\frac{1}{p-1}}, u_2(x,T) &\\sim & \\frac{2 p}{(p-1)^2} \\left[ \\frac{ (p-1)^2|x-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07183","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"}