A free boundary problem in lubrication theory

A new numerical approach of a lubrication free boundary problem

A combination of a semidiscretized scheme and an iterative method is applied to a free boundary problem. The considered problem is issued from a cavitation model in lubrication theory and treats on the determination of the cavitation area. Estimates L∞(Ω) which provide the convergence of the approximated solution is obtained. Finally, some numerical test examples are presented to illustrate the...

About an inverse problem for a free boundary compressible problem in hydrodynamic lubrication

In this paper an inverse problem is considered for a non coercive partial differential equation, issued from a mass conservation cavitation model for a slightly compressible fluid. The cavitation phenomenon and compressibility take place and are described by the Elrod model. The existence of an optimal solution is proven. Optimality conditions are derived and some numerical results are given.

Homogenization of a nonlocal elastohydrodynamic lubrication problem: a new free boundary model

A Free { Boundary Problem in Dermal Drug

In this paper we study a free{boundary problem in a multicomponent domain. Our study was motivated by the mathematical modelling of dermal and transdermal drug delivery, where the multilayered skin model was considered. At the interface connecting two components the conservation of the ux and Nernst's distribution law hold and it is supposed that in any component there is a positive minimum con...

A two-phase free boundary problem for a semilinear elliptic equation

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...