{"paper":{"title":"Construction and Stability of type I blowup solutions for non-variational semilinear parabolic systems","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":"2018-08-15T17:59:40Z","abstract_excerpt":"We consider in this note the semilinear heat system $$\\partial_t u = \\Delta u + f(v), \\quad \\partial_t v = \\mu\\Delta v + g(u), \\quad \\mu > 0,$$ where the nonlinearity has no gradient structure taking of the particular form $$f(v) = v|v|^{p-1} \\quad \\text{and}\\quad g(u) = u|u|^{q-1} \\quad \\text{with} \\quad p, q > 1, $$ or\n  $$f(v) = e^{pv}\\quad \\text{and} \\quad g(u) = e^{qu} \\quad \\text{with} \\quad p,q > 0.$$ We exhibit type I blowup solutions for this system and give a precise description of its blowup profiles. The method relies on two-step procedure: the reduction of the problem to a finite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05211","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"}