Abstract
The existence of solution to membrane shell equation is studied in a bounded open connected domain ω (Lipschitzian when ω has a boundary γ) in a C 1,1 midsurface for homogeneous Neumann boundary conditions or homogeneous Dirichlet boundary conditions on a part γ0 ofγ. It is proved that its tangential part is solution of the reduced membrane shell equation in H 1(ω)N (resp. H 1 γ0(ω)N) unique up to an element of a finite dimensional subspace, while its normal component belongs to a weighed L 2(ω) space by the pointwise norm of the second fundamental form. It is also shown that the reduced equation is equivalent to the equation for the projection onto the linear subspace of vector functions whose linear change of metric tensor is orthogonal to the second fundamental form of the midsurface.
This research has been supported by National Sciences and Engineering Research Council of Canada research grant A-8730 and by a FCAR grant (Ministère de l’Éducation du Québec).
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35359-3_40
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Keywords
- Equivalence Class
- Variational Equation
- Fundamental Form
- Homogeneous Dirichlet Boundary Condition
- Finite Dimensional Subspace
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Delfour, M.C. (1999). Membrane Shell Equation: Characterization of the Space of Solutions. In: Chen, S., Li, X., Yong, J., Zhou, X.Y. (eds) Control of Distributed Parameter and Stochastic Systems. IFIP Advances in Information and Communication Technology, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35359-3_3
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