We consider a system of partial differential equations describing mass transport in multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick–Onsager or Maxwell–Stefan closure approach. Mechanical forces result into one single convective mixture velocity, barycentric one, which obeys Navier–Stokes equations. thermodynamic pressure is defined by Gibbs–Duhem equation. Chemi...

We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely ...

A boundary element formulation for the solution of multiple moving boundary problems is presented and tested herein. A heat transfer problem involving heating of solid, melting of solid and vaporisation of liquid is considered. Numerical results show that the boundary element method is more suitable and more accurate than both finite difference and finite element methods for this kind of problems

We introduce and discuss the Homotopy perturbation method, the Adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. Then, we give an example of the stefan problem with  kinetics and solve it by these methods.

We prove the existence of at least two solutions for a fourth order equation, which includes the vortex equations for the U(1) and CP (1) self-dual Maxwell-Chern-Simons models as special cases. Our method is variational, and it relies on an “asymptotic maximum principle” property for a special class of supersolutions to this fourth order equation.

We study the approximate controllability of the stochastic Maxwell equations with an abstract approach and a constructive approach using a generalization of the Hilbert uniqueness method as proposed in Kim (2004, Approximate controllability of a stochastic wave equation. Appl. Math. Optim., 49, 81–98) for the stochastic wave equation.

The two-dimensional Vlasov–Maxwell system, for a plasma with mobile, magnetised electrons and ions, is investigated numerically. A previously developed method for solving the two-dimensional electrostatic Vlasov equation, Fourier transformed in velocity space, for mobile electrons and with ions fixed in space, is generalised to the fully electromagnetic, two-dimensional Vlasov–Maxwell system fo...

In this paper we study a Landau-Lifshitz equation in ferromagnetism without exchange energy as a quasi-stationary limit of a coupled Maxwell system as dielectric permittivity approaches zero. We present a different formulation and proof of this quasi-stationary limit result. We also prove a new uniqueness and stability result for the limit Landau-Lifshitz equation.

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed ...