Advances in Differential Equations

Limit behaviors of some boundary value problems with high and/or low valued parameters

Salima Hassani, Abderrahman Maghnouji, and Serge Nicaise

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The first aim of this paper is to give a general variational framework for bilinear forms depending on two parameters tending to zero and to infinity respectively, allowing us to analyze the three limit problems. Secondly, we give different illustrative applications for transmission problems involving some elasticity systems, diffusion problems, and Maxwell systems where one parameter tends to infinity and/or a part of the domain squeezes to a smooth surface. These limit procedures lead to new transmission problems, like a coupling between the Lamé system and the Stokes system.

Article information

Adv. Differential Equations, Volume 14, Number 9/10 (2009), 875-910.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations 35R05: Partial differential equations with discontinuous coefficients or data


Hassani, Salima; Nicaise, Serge; Maghnouji, Abderrahman. Limit behaviors of some boundary value problems with high and/or low valued parameters. Adv. Differential Equations 14 (2009), no. 9/10, 875--910.

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