{"paper":{"title":"Dispersive estimates for wave-type equations with time-dependent damping","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Halit Sevki Aslan, Marcelo Rempel Ebert","submitted_at":"2026-06-09T16:51:30Z","abstract_excerpt":"In this paper, we study the Cauchy problem for a class of semilinear evolution equations with scale-invariant time-dependent dissipation \\begin{equation*} \\begin{cases} u_{tt} + L_{w^2}u + \\dfrac{\\mu}{1+t}u_t = \\Delta^{\\theta} f(u), & t>0,\\ x\\in\\mathbb{R}^n,\\\\ u(0,x) = 0,\\qquad u_t(0,x) = u_1(x), & x\\in\\mathbb{R}^n, \\end{cases} \\end{equation*} where $\\mu>0$, $f(u)=|u|^\\alpha$ with $\\alpha>1$, $\\theta\\in\\{0,1\\}$, and the operator $L_{w^2}$ is defined on the Fourier transform by multiplication by $w(\\xi)^2$. We prove the global (in time) existence of small data solutions for $\\alpha>\\alpha_{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11093","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/2606.11093/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"}