{"paper":{"title":"F. John's stability conditions vs. A. Carasso's SECB constraint for backward parabolic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Dongwoo Sheen, Jinwoo Lee","submitted_at":"2009-01-29T14:27:02Z","abstract_excerpt":"In order to solve backward parabolic problems F. John [{\\it Comm. Pure. Appl. Math.} (1960)] introduced the two constraints \"$\\|u(T)\\|\\le M$\" and $\\|u(0) - g \\| \\le \\delta$ where $u(t)$ satisfies the backward heat equation for $t\\in(0,T)$ with the initial data $u(0).$\n  The {\\it slow-evolution-from-the-continuation-boundary} (SECB) constraint has been introduced by A. Carasso in [{\\it SIAM J. Numer. Anal.} (1994)] to attain continuous dependence on data for backward parabolic problems even at the continuation boundary $t=T$. The additional \"SECB constraint\" guarantees a significant improvement"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4613","kind":"arxiv","version":2},"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"}