{"paper":{"title":"Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Self-similar solutions of the associated parabolic problem are asymptotically stable for the semilinear beam equation with two variable coefficients in the subcritical case.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mohamed Ali Hamza, Shuji Yoshikawa, Yuta Wakasugi","submitted_at":"2026-05-01T10:04:59Z","abstract_excerpt":"In this article, we investigate the asymptotic profile of solutions to the Cauchy problem for a nonlinear beam equation with two variable coefficients in the subcritical nonlinear case. In contrast to our previous result [6], in which the asymptotic profile is governed by the linear heat kernel and the nonlinear effect is asymptotically negligible, the asymptotic profile in the present setting is described by a self-similar solution to the associated nonlinear parabolic equation (constructed in Brezis-Peletier-Terman [1]). The proof relies on delicate energy estimates in weighted spaces formul"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove an asymptotic stability result of self-similar solutions of the associated parabolic problem.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The semilinear beam equation with two variable coefficients admits the required weighted energy estimates in parabolic self-similar variables in the subcritical case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves asymptotic stability of self-similar solutions for the semilinear beam equation in the subcritical case using fine energy estimates in weighted spaces rewritten in parabolic self-similar variables.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Self-similar solutions of the associated parabolic problem are asymptotically stable for the semilinear beam equation with two variable coefficients in the subcritical case.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b0ad0a1fd2a97d98863fc6573227fc665394a7aca06e70b3455fc4e5baf5b026"},"source":{"id":"2605.00550","kind":"arxiv","version":2},"verdict":{"id":"0269b2df-3df4-495b-9a62-8a71fd63f1c6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T19:24:08.202377Z","strongest_claim":"We prove an asymptotic stability result of self-similar solutions of the associated parabolic problem.","one_line_summary":"Proves asymptotic stability of self-similar solutions for the semilinear beam equation in the subcritical case using fine energy estimates in weighted spaces rewritten in parabolic self-similar variables.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The semilinear beam equation with two variable coefficients admits the required weighted energy estimates in parabolic self-similar variables in the subcritical case.","pith_extraction_headline":"Self-similar solutions of the associated parabolic problem are asymptotically stable for the semilinear beam equation with two variable coefficients in the subcritical case."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00550/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T19:40:07.013309Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:04:03.719525Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"bb7ecea8bdd1981cc90ae8b592e938bab8d4a27b31fdc9b24188fde26af2b19b"},"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"}