We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell’s equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell-Loren...

The Fisher-Stefan model involves solving the Fisher-KPP equation on a domain whose boundary evolves according to Stefan-like condition. alleviates two practical limitations of standard when applied biological invasion. First, unlike equation, solutions have compact support, enabling one define interface between occupied and unoccupied regions unambiguously. Second, admits for which population b...

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 ...

Highlights • GENERIC description of homogeneous mixtures that flow with multiple independent velocities, several temperatures, and electromagnetic field The is reduced to the case only one momentum (classical irreversible thermodynamics), generalizing Maxwell-Stefan diffusion equations generalised are mechanical equilibrium (no momentum) thus a non-isothermal variant dusty gas model derived tem...

Numerical simulation of gas flow in porous media is becoming increasingly attractive due to its importance shale and natural production carbon dioxide sequestration. In this paper, taking molar densities as the primary unknowns rather than pressure fractions, we propose an alternative formulation multicomponent Maxwell–Stefan (MS) model with rock compressibility. Benefiting from definitions sol...

Abstract Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a pair of matrix equations. We present a matrix representation of the Maxwell equation in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires 8×8 matrices and...

Dissipative effects in electromagnetism on macroscopic scales are examined by coarse-graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are ...