{"paper":{"title":"A note on a weakly coupled system of semi-linear visco-elastic damped $\\sigma$-evolution models with different power nonlinearities and different $\\sigma$ values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tuan Anh Dao","submitted_at":"2018-10-21T16:53:37Z","abstract_excerpt":"In this article, we prove the global (in time) existence of small data solutions from energy spaces basing on $L^q$ spaces, with $q \\in (1,\\infty)$, to the Cauchy problems for a weakly coupled system of semi-linear visco-elastic damped $\\sigma$-evolution models. Here we consider different power nonlinearities and different $\\sigma$ values in the comparison between two single equations. To do this, we use $(L^m \\cap L^q)- L^q$ and $L^q- L^q$ estimates, i.e., by mixing additional $L^m$ regularity for the data on the basis of $L^q- L^q$ estimates for solutions, with $m \\in [1,q)$, to the correspo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09664","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"}