and Applied Analysis 3 Theorem 1.1. Let n0, p0 ∈ L1 R2 ∩ L logL R2 , n0, p0 ≥ 0 in R2, ∫ n0 dx ∫ p0 dx,∇φ0 ∈ L2, and u0 ∈ L2. Then there exists a unique weak solution u, n, p, φ to the problem 1.1 – 1.6 satisfying ( n, p ) ∈ L∞0, T ;L1 ∩ L logL ∩ L20, T ;L2 ∩ L4/30, T ;W1,4/3, n, p ≥ 0 in R2 × 0, T ( ∂tn, ∂tp ) ∈ L4/30, T ;W−1,4/3, ∇φ ∈ L∞0, T ;L2 ∩ L20, T ;H1 ∩ L40, T ;L4, u ∈ L∞0, T ;L2 ∩ L20...

Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviours contingent on field strength and material properties. These phenomena are best described by the Melcher–Taylor leaky dielectric model, which hypothesizes charge accumulation on the drop–fluid interface and prescribes a bal...

In this study, a multiphysical description of fluid transport through osteo-articular porous media is presented. Adapted from the model of Moyne and Murad, which is intended to describe clayey materials behaviour, this multiscale modelling allows for the derivation of the macroscopic response of the tissue from microscopical information. First the model is described. At the pore scale, electroh...

Realistic boundaries of finite heat conductivity for thermoconvection in a Rayleigh-Bénard setup with magnetized ferrofluids are investigated. A linear stability analysis of the conductive state is performed with a shooting method. It shows that the critical wave number is for any magnetic field stronly influenced by the conductivity of the boundaries. Linear as well as nonlinear coefficients o...