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A boundary multivalued integral “equation” approach to the semipermeability problem

Jaroslav Haslinger, Charalambos C. Baniotopoulos, Panagiotis D. Panagiotopoulos (1993)

Applications of Mathematics

The present paper concerns the problem of the flow through a semipermeable membrane of infinite thickness. The semipermeability boundary conditions are first considered to be monotone; these relations are therefore derived by convex superpotentials being in general nondifferentiable and nonfinite, and lead via a suitable application of the saddlepoint technique to the formulation of a multivalued boundary integral equation. The latter is equivalent to a boundary minimization problem with a small...

A mixed formulation of a sharp interface model of stokes flow with moving contact lines

Shawn W. Walker (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking...

An example in the gradient theory of phase transitions

Camillo De Lellis (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals ∫ Ω ε | ∇ 2 u | 2 + ( 1 - | ∇ u | 2 ) 2 / ε is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.

An example in the gradient theory of phase transitions

Camillo De Lellis (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals ∫ Ω ε | ∇ 2 u | 2 + ( 1 - | ∇ u | 2 ) 2 / ε is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.

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