{"paper":{"title":"Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Irena Lasiecka, Xiaojun Wang","submitted_at":"2015-05-28T01:30:36Z","abstract_excerpt":"We are interested in the Moore-Gibson-Thompson(MGT) equation with memory \\begin{equation}\\nonumber \\tau u_{ttt}+ \\alpha u_{tt}+c^2\\A u+b\\A u_t -\\int_0^tg(t-s)\\A w(s)ds=0. \\end{equation} We first classify the memory into three types. Then we study how a memory term creates damping mechanism and how the memory causes energy decay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07523","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"}