Asymptotic Analysis - Volume 12, issue 3

Authors: Sablè-Tougeron, Monique

Article Type: Research Article

Abstract: We suggest a justification for all time of the formal development of geometric optics, for a conservative, genuinely nonlinear, initial-boundary value problem, in case of BV data with compact support and function of slow variables.

DOI: 10.3233/ASY-1996-12301

Citation: Asymptotic Analysis, vol. 12, no. 3, pp. 169-186, 1996

Authors: Lods, V.

Article Type: Research Article

Abstract: We consider a shell, when first the thickness approaches zero and then the middle surface becomes flat. As noted by P.G. Ciarlet, the limit displacement obtained in this fashion is different from the limit displacement obtained when the shell becomes a plate first. Indeed, the ‘membrane’ and ‘bending’ effects both appear when first the shell becomes a plate, while only one of these effects appear when first the thickness approaches zero. This result is proved for shells with uniformly elliptic middle surfaces and for cylindrical shells.

DOI: 10.3233/ASY-1996-12302

Citation: Asymptotic Analysis, vol. 12, no. 3, pp. 187-211, 1996

Authors: Figueiredo, Isabel | Zuazua, Enrique

Article Type: Research Article

Abstract: We consider the exact controllability problem for a three-dimensional linear elastic thin plate, with thickness 2ε and a polygonal middle surface. Controls are imposed on the lateral surface and at the top and bottom of the plate. The asymptotic limit when ε→0 is computed. We obtain that the displacements converge to a controlled Kirchhoff–Love displacement, where the normal displacement satisfies the usual two-dimensional evolution equation for a linear plate, with controls on the boundary and in the interior of the plate.

DOI: 10.3233/ASY-1996-12303

Citation: Asymptotic Analysis, vol. 12, no. 3, pp. 213-252, 1996

Article Type: Other

Citation: Asymptotic Analysis, vol. 12, no. 3, pp. 253-258, 1996