{"paper":{"title":"Global existence of solutions for semi-linear wave equation with scale-invariant damping and mass in exponentially weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Palmieri","submitted_at":"2017-08-02T13:32:46Z","abstract_excerpt":"In this paper we consider the following Cauchy problem for the semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity: \\begin{align}\\label{CP abstract} \\begin{cases} u_{tt}-\\Delta u+\\dfrac{\\mu_1}{1+t} u_t+\\dfrac{\\mu_2^2}{(1+t)^2}u=|u|^p, \\\\ u(0,x)=u_0(x), \\,\\, u_t(0,x)=u_1(x), \\end{cases}\\tag{$\\star$} \\end{align} where $\\mu_1, \\mu_2^2$ are nonnegative constants and $p>1$. On the one hand we will prove a global (in time) existence result for \\eqref{CP abstract} under suitable assumptions on the coefficients $\\mu_1, \\mu_2^2$ of the damping and the mass term a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00738","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"}