{"paper":{"title":"On the MGT equation with memory of type II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Dell'Oro, Irena Lasiecka, Vittorino Pata","submitted_at":"2019-04-17T11:43:47Z","abstract_excerpt":"We consider the Moore-Gibson-Thompson equation with memory of type II $$ \\partial_{ttt} u(t) + \\alpha \\partial_{tt} u(t) + \\beta A \\partial_t u(t) + \\gamma Au(t)-\\int_0^t g(t-s) A \\partial_t u(s){\\rm d} s=0 $$ where $A$ is a strictly positive selfadjoint linear operator (bounded or unbounded) and $\\alpha,\\beta,\\gamma>0$ satisfy the relation $\\gamma\\leq\\alpha\\beta$. First, we prove a well-posedness result without requiring any restriction on the total mass $\\varrho$ of $g$. Then we show that it is always possible to find memory kernels $g$, complying with the usual mass restriction $\\varrho<\\be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08203","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"}