Ben Kiran, Taoufiq On a singular perturbation problem. I: Elasticity. (Research announcement). (Sur un problème de perturbation singulière. I: Elasticité.) (French) Zbl 1047.34512 Extr. Math. 8, No. 2-3, 142-147 (1993). The author considers the singular perturbation problem \(\varepsilon^2(u_{\varepsilon}^{(4)}- u_{\varepsilon}^{(2)})- u_{\varepsilon}^{(2)}+ u_{\varepsilon}=f\), \(0<x<\pi\) subject to some boundary conditions at \(x=0\) and at \(x=\pi\). This problem arises in elasticity theory. The paper deals with the convergence of \(u_{\varepsilon}\) when \(f\) is in the Sobolev space \(H^{\beta}((0,\pi))\), \(\beta>\frac12\). It is shown that the limit function solves the problem \(-u''+u=f\), \(u(0)=u(\pi)=0\). Reviewer: Abdelkader Boucherif (Dhahran) Cited in 1 Review MSC: 34E15 Singular perturbations for ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations 74B05 Classical linear elasticity 34E10 Perturbations, asymptotics of solutions to ordinary differential equations Keywords:singular perturbation; fourth-order two-point boundary value problems; elasticity PDFBibTeX XMLCite \textit{T. Ben Kiran}, Extr. Math. 8, No. 2--3, 142--147 (1993; Zbl 1047.34512) Full Text: EuDML