{"paper":{"title":"Construction and stability of blowup solutions for a non-variational semilinear parabolic system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Tej-Eddine Ghoul, Van Tien Nguyen","submitted_at":"2016-10-31T12:00:12Z","abstract_excerpt":"We consider the following parabolic system whose nonlinearity has no gradient structure: $$\\left\\{\\begin{array}{ll} \\partial_t u = \\Delta u + |v|^{p-1}v, \\quad & \\partial_t v = \\mu \\Delta v + |u|^{q - 1}u,\\\\ u(\\cdot, 0) = u_0, \\quad & v(\\cdot, 0) = v_0, \\end{array}\\right. $$ in the whole space $\\mathbb{R}^N$, where $p, q > 1$ and $\\mu > 0$. We show the existence of initial data such that the corresponding solution to this system blows up in finite time $T(u_0, v_0)$ simultaneously in $u$ and $v$ only at one blowup point $a$, according to the following asymptotic dynamics: $$\\left\\{\\begin{array"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09883","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"}