The weak-strong uniqueness for Maxwell--Stefan systems and some generalized is proved. corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. key points of the proofs various inequalities relative entropy associated analysis spectrum quadratic form capturing frictional dissipation. latter task complicated by singular nature diffusi...

The global-in-time existence of bounded weak solutions to the Maxwell–Stefan–Fourier equations in Fick–Onsager form is proved. model consists mass balance for partial densities and energy equation total energy. diffusion heat fluxes depend linearly on gradients thermo-chemical potentials gradient temperature include Soret Dufour effects. cross-diffusion system exhibits an entropy structure, whi...

We investigate the diffusion asymptotics of Boltzmann equation for gaseous mixtures, in perturbative regime around a local Maxwellian vector whose fluid quantities solve flux-incompressible Maxwell–Stefan system. Our framework is torus and we consider hard-potential collision kernels with angular cutoff. As opposed to existing results about hydrodynamic limits mono-species case, study here not ...

For a linear transport equation in one space dimension with speeds in a compact interval and a general symmetric kernel for the change of velocity a problem with free boundary (Stefan problem) is stated. The case of constant speed corresponds to a Stefan problem for the damped wave equation (telegraphers equation). Existence and uniqueness of the free boundary is shown, and the connection to th...

We present the Onsager–Stefan–Maxwell thermodiffusion equations, which account for Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves structure of isothermal Stefan–Maxwell separating thermodynamic forces that drive diffusion force drives heat flow. The transport-coefficient matrix is symmetric, second law thermodynamic...

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.

Abstract We investigate structure-preserving finite element discretizations of the steady-state Stefan–Maxwell diffusion problem, which governs mass transport within a phase consisting multiple species. An approach inspired by augmented Lagrangian methods allows us to construct symmetric positive definite Onsager matrix, in turn leads an effective numerical algorithm. prove inf-sup conditions f...

The general form of the Stefan-Boltzmann law for the energy density of black-body radiation is generalized to a spacetime with extra dimensions using standard kinetic and thermodynamic arguments. From statistical mechanics one obtains an exact formula. In a field-theoretic derivation, the Maxwell field must be quantized. The notion of electric and magnetic fields is different in spacetimes with...

In this study, a mathematical model is introduced to simulate the coupled heat transfer equation and Stefan condition occurring in moving boundary problems such as the solidification process in the continuous casting machines. In the continuous casting process, there exists a two-phase Stefan problem with moving boundary. The control-volume finite difference approach together with the boundary ...