We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions, we construct a smooth approximation of the global solution of the Stefan problem with undercooling, which, until the contact, gives the classical solution mentioned abo...

In this work, we are interested in two different diffusion models for multicomponent mixtures. We numerically recover experimental results underlining the inadequacy of the usual Fick diffusion model, and the importance of using the Maxwell-Stefan model in various situations. This model nonlinearly couples the mole fractions and the fluxes of each component of the mixture. We then consider a su...

In dimension three, we establish the existence of weak solutions {u,H,E} to the Landau-Lifshitz equation (1.1) coupled with the time-dependent Maxwell equation (1.2)-(1.3) such that u is Hölder continuous away from a closed set Σ, which has locally finite 3-dimensional parabolic Hausdorff measure. For two reduced Maxwell equations (1.17) and (1.18), Hölder continuity of ∇u away from Σ is also e...

A lattice Boltzman model for the simulation of binary mixtures is presented. Contrary to previous models, the present formulation is able to simulate mixtures with different Schmidt numbers and arbitrary molecular mass ratio of the components. In the hydrodynamic limit, the Navier-Stokes and the Stefan-Maxwell binary diffusion equations are recovered. The model is used for the simulation of bin...

A model for the simulation of the steady-state impedance response of a polymer electrolyte membrane fuel cell ~PEMFC! cathode is presented. The catalyst layer of the electrode is assumed to consist of many flooded spherical agglomerate particles surrounded by a small volume fraction of gas pores. Stefan-Maxwell equations are used to describe the multicomponent gas-phase transport occurring in b...

This paper presents the simulations for a two-dimensional PEMFC with an interdigitated flow channel design using FEMLAB. The multi-species flow of O2, H2, H2O and inert N2 is examined over the entire fuel cell working range. The transportations of these gases in the porous anode/cathode are predicted using the Maxwell-Stefan transport equations and the Fick’s law; the flow field is predicted us...

Keywords: Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation a b s t r a c t We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the he...

Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. In an earlier paper [1] it has been shown that in the case of a beam with uniform phase space density the Vlasov-Maxwell equations can be replaced exactly by the macroscopic w...

We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions , we construct a smooth approximation of the global solution of the Stefan problem with undercooling, which, until the contact, gives the classical solution mentioned ab...

Due to the mathematical complexity of the Boltzmann equation for inelastic hard spheres, a kinetic model has recently been proposed whereby the collision rate (which is proportional to the relative velocity for hard spheres) is replaced by an average velocity-independent value. The resulting inelastic Maxwell model has received a large amount of recent interest, especially in connection with th...