{"paper":{"title":"An application of $L^m-L^r$ estimates to weakly coupled systems of semilinear viscoelastic wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenhui Chen, Yan Liu","submitted_at":"2018-09-20T08:30:53Z","abstract_excerpt":"We consider weakly coupled systems of semilinear viscoelastic wave equations with different power source nonlinearities in $\\mathbb{R}^n$, $n\\geq1$ as follows: \\begin{equation*} \\left\\{\\begin{aligned} &u_{tt}-\\Delta u+g\\ast\\Delta u+u_t=|\\partial_t^{\\ell}v|^p,\\\\ &v_{tt}-\\Delta v+g\\ast\\Delta v+v_t=|\\partial_t^{\\ell}u|^q,\\\\ \\end{aligned}\\right. \\end{equation*} with $\\ell=0,1$ and $p,q>1$. After presenting $L^m-L^r$ estimates with $1\\leq m\\leq r\\leq \\infty$ of solutions to the corresponding linearized problem with vanishing right-hand side, we prove the existence of global in time solutions to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07525","kind":"arxiv","version":3},"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"}