{"paper":{"title":"Infinite energy solutions for critical wave equation with fractional damping in unbounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anton Savostianov","submitted_at":"2015-11-14T18:24:01Z","abstract_excerpt":"This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\\mathbb{R}^3$ with fractional damping of the form $(-\\Delta_x+1)^\\frac{1}{2}\\partial_t u$. The work extends previously known results for bounded domains in finite energy case. Furthermore, well-posedness and existence of locally-compact smooth attractors for the critical quintic non-linearity are obtained under less restrictive assumptions on non-linearity, relaxing some artificial technical conditions used before. This is achieved by virtue of new type Lyapunov functional that allow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04592","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"}