{"paper":{"title":"Finite-time blowup for a complex Ginzburg-Landau equation with linear driving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Paulo Dias, M\\'ario Figueira, Thierry Cazenave","submitted_at":"2013-10-01T09:00:04Z","abstract_excerpt":"In this paper, we consider the complex Ginzburg--Landau equation $u_t = e^{i\\theta} [\\Delta u + |u|^\\alpha u] + \\gamma u$ on ${\\mathbb R}^N $, where $\\alpha >0$, $\\gamma \\in \\R$ and $-\\pi /2<\\theta <\\pi /2$. By convexity arguments we prove that, under certain conditions on $\\alpha ,\\theta ,\\gamma $, a class of solutions with negative initial energy blows up in finite time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0191","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"}