Related papers: Cross-diffusion limits in multispecies kinetic mod…
In this paper, we study the hydrodynamic limit transition from the Boltzmann equation for gas mixtures to the two-fluid macroscopic system. Employing a meticulous dimensionless analysis, we derive several novel hydrodynamic models via the…
The Kramers problem for quantum Bose-gases with specular-diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers' problem the new generalized method of a source of the decision of the boundary problems from…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
The thermalization of a gas towards a Maxwellian velocity distribution with the background temperature is described by a kinetic relaxation model. The sum of the kinetic energy of the gas and the thermal energy of the background are…
The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale fluid dynamic equations, such as the Boltzmann and Navier-Stokes…
Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet,…
A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the…
We study an initial boundary value problem for a cross-diffusion system in population dynamics. The mathematical challenge is due to the fact that the determinant of the coefficient matrix of the system changes signs. As a result, the…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely…
In this short note, we review a recently developed method for analysing multi-component driven diffusive systems with open boundaries. The approach generalises the extremal-current principle known for single-component models and is based on…
Singular limit problems of reaction-diffusion systems have been studied in cases where the effects of the reaction terms are very large compared with those of the other terms. Such problems appear in literature in various fields such as…
In this paper, we propose a lattice Boltzmann (LB) model for the generalized coupled cross-diffusion-fluid system. Through the direct Taylor expansion method, the proposed LB model can correctly recover the macroscopic equations. The cross…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…
To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…
We consider kinetic and related macroscopic equations on networks. A class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given by the wave equation. Coupling conditions for the macroscopic…
When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow---an observation attributed to the thermo-stress convection effects at microscale. The…
In the present contribution, we derive from kinetic theory a unified fluid model for multicomponent plasmas by accounting for the electromagnetic field influence. We deal with a possible thermal nonequilibrium of the translational energy of…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…