Stability analysis of abstract systems of Timoshenko type
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We consider an abstract system of Timoshenko type$$\begin{aligned} \left\{ {\begin{array}{l} \rho_1{{\ddot \varphi}} + a A^{\frac12}(A^{\frac12}\varphi + \psi) =0\\\rho_2{{\ddot \psi}} + b A \psi + a (A^{\frac12}\varphi + \psi) -\delta A^\gamma {\theta} = 0\\\rho_3{{\dot \theta}} + c A\theta + \delta A^\gamma {{\dot \psi}} =0 \end{array}} \right. \end{aligned}$$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 \({S(t)}\) when the spectrum of the leading operator \({A}\) does not consist of eigenvalues only.KeywordsTimoshenko systemContraction semigroupSpectral theoryStabilitySemiuniform stabilityExponential stabilityMathematics Subject Classification35B3535P0547D05References1.Ammar-Khodja F., Bader A., Benabdallah A.: Dynamic stabilization of systems via decoupling techniques. ESAIM Control Optim. Calc. Var. 4, 577–593 (1999)MathSciNetCrossRefMATHGoogle Scholar2.Arendt W., Batty C.J.K.: Tauberian theorems and stability of one-parameter semigroups. Trans. Amer. Math. Soc. 306, 837–852 (1988)MathSciNetCrossRefMATHGoogle Scholar3.Arendt W., Batty C.J.K., Hieber M., Neubrander F.: Vector-valued Laplace transforms and Cauchy problems. Birkhäuser, Basel (2011)CrossRefMATHGoogle Scholar4.C.J.K. 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Magazine 41, 744–746 (1921)CrossRefGoogle ScholarCopyright information© Springer International Publishing 2016Authors and AffiliationsValeria Danese1Filippo Dell’Oro1Email authorVittorino Pata11.Politecnico di Milano - Dipartimento di MatematicaMilanItaly About this article CrossMark Print ISSN 1424-3199 Online ISSN 1424-3202 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00028-015-0314-2_Stability analysis of abstract sys", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00028-015-0314-2_Stability analysis of abstract sys", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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