Displaying similar documents to “On the membrane approximation for thin elastic shells in the hyperbolic case.”

Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case

Philippe Karamian, Jacqueline Sanchez-Hubert, Évariste Sanchez Palencia (2002)

International Journal of Applied Mathematics and Computer Science

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We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution. ...

Symmetric hyperbolic systems with boundary conditions that do not satisfy the Kreiss-Sakamoto condition

Matthias Eller (2008)

Applicationes Mathematicae

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Symmetric hyperbolic systems with a class of non-homogeneous boundary conditions that do not satisfy the Kreiss-Sakamoto condition (or uniform Lopatinskii condition) are discussed. The boundary conditions are of conservative type. An energy estimate which provides interior and boundary regularity for weak solutions to the system is proved. The results are valid for operators with rough coefficients. As an example the anisotropic Maxwell system is considered.

Curves and surfaces in hyperbolic space

Shyuichi Izumiya, Donghe Pei, Masatomo Takahashi (2004)

Banach Center Publications

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In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

On the change of energy caused by crack propagation in 3-dimensional anisotropic solids

Martin Steigemann, Maria Specovius-Neugebauer (2014)

Mathematica Bohemica

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Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows...