{"paper":{"title":"Paving the way to a $\\operatorname{T}$-coercive method for the wave equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Carolina Urz\\'ua-Torres, Daniel Hoonhout, Richard L\\\"oscher","submitted_at":"2025-09-02T13:08:16Z","abstract_excerpt":"In this paper, we take a first step toward introducing a space-time transformation operator $\\operatorname{T}$ that establishes $\\operatorname{T}$-coercivity for the weak variational formulation of the wave equation in space and time on bounded Lipschitz domains. As a model problem, we study the ordinary differential equation (ODE) $u'' + \\mu u = f$ for $\\mu>0$, which is linked to the wave equation via a Fourier expansion in space. For its weak formulation, we introduce a transformation operator $\\operatorname{T}_\\mu$ that establishes $\\operatorname{T}_\\mu$-coercivity of the bilinear form yiel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02288","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.02288/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}