Displaying similar documents to “On the structure of layers for singularly perturbed equations in the case of unbounded energy”

On the structure of layers for singularly perturbed equations in the case of unbounded energy

E. Sanchez–Palencia (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider singular perturbation variational problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε → 0. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral...

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. ...

A multiscale correction method for local singular perturbations of the boundary

Marc Dambrine, Grégory Vial (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution u of a second order elliptic equation posed in the perturbed domain with respect to the size parameter of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of u based on a multiscale superposition of the unperturbed solution and a profile defined...