{"paper":{"title":"Stability analysis of abstract systems of Timoshenko type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Dell'Oro, Valeria Danese, Vittorino Pata","submitted_at":"2015-04-03T10:51:23Z","abstract_excerpt":"We consider an abstract system of Timoshenko type $$ \\begin{cases} \\rho_1{{\\ddot \\varphi}} + a A^{\\frac12}(A^{\\frac12}\\varphi + \\psi) =0\\\\ \\rho_2{{\\ddot \\psi}} + b A \\psi + a (A^{\\frac12}\\varphi + \\psi) - \\delta A^\\gamma {\\theta} = 0\\\\ \\rho_3{{\\dot \\theta}} + c A\\theta + \\delta A^\\gamma {{\\dot \\psi}} =0 \\end{cases} $$ where the operator $A$ is strictly positive selfadjoint. For any fixed $\\gamma\\in\\mathbb{R}$, the stability properties of the related solution semigroup $S(t)$ are discussed. In particular, a general technique is introduced in order to prove the lack of exponential decay of $S(t)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00804","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"}