{"paper":{"title":"An application of $L^1$ estimates for oscillating integrals to parabolic like semi-linear structurally damped $\\sigma$-evolution models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Reissig, Tuan Anh Dao","submitted_at":"2018-08-08T10:11:01Z","abstract_excerpt":"We study the following Cauchy problems for semi-linear structurally damped $\\sigma$-evolution models: \\begin{equation*} u_{tt}+ (-\\Delta)^\\sigma u+ \\mu (-\\Delta)^\\delta u_t = f(u,u_t),\\, u(0,x)= u_0(x),\\, u_t(0,x)=u_1(x) \\end{equation*} with $\\sigma \\ge 1$, $\\mu>0$ and $\\delta \\in (0,\\frac{\\sigma}{2})$. Here the function $f(u,u_t)$ stands for the power nonlinearities $|u|^{p}$ and $|u_t|^{p}$ with a given number $p>1$. We are interested in investigating $L^{1}$ estimates for oscillating integrals in the presentation of the solutions to the corresponding linear models with vanishing right-hand "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02706","kind":"arxiv","version":2},"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"}