Geodesic
On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs
Applications of Mathematics, Tome 23 (1978) no. 2, pp. 132-149.

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The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space $W(\Omega)\subset H^1_0(\Omega)\times H^1_0(\Omega) \times H^2_0(\Omega)$, on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space $Q(\Omega)$.
DOI : 10.21136/AM.1978.103737
Classification : 49L99, 65N30, 74K25, 74S05
Keywords: numerical analysis; weak solution; boundary value problem; shallow shell; variational problem; finite elements 
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     title = {On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs},
     journal = {Applications of Mathematics},
     pages = {132--149},
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Bock, Igor; Lovíšek, Ján. On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs. Applications of Mathematics, Tome 23 (1978) no. 2, pp. 132-149. doi : 10.21136/AM.1978.103737. http://geodesic.mathdoc.fr/articles/10.21136/AM.1978.103737/

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