{"paper":{"title":"Improved conditions for single-point blow-up in reaction-diffusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nejib Mahmoudi, Philippe Souplet, Slim Tayachi","submitted_at":"2015-01-21T10:17:23Z","abstract_excerpt":"We study positive blowing-up solutions of the system: $$u_{t}-\\delta\\Delta u=v^p,\\,\\,\\, v_{t}-\\Delta v=u^{q},$$ as well as of some more general systems. For any $p,\\,q>1$, we prove single-point blow-up for any radially decreasing, positive and classical solution in a ball. This improves on previously known results in 3 directions:\n  (i) no type I blow-up assumption is made (and it is known that this property may fail);\n  (ii) no equidiffusivity is assumed, i.e. any $\\delta>0$ is allowed;\n  (iii) a large class of nonlinearities $F(u,v)$, $G(u,v)$ can be handled, which need not follow a precise "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05112","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"}