Related papers: Quasineutral limit of the electro-diffusion model …
We derive a Debye-H\"uckel-like model of the electric ion-ion interaction for non-constant dielectric susceptibility, which does not depend on any kind of charging process due to its foundation in the general framework of non-equilibrium…
This work is concerned with the quasineutral limit of the Vlasov-Poisson system in two and three dimensions. We justify the formal limit for very small but rough perturbations of analytic initial data, generalizing the results of \cite{HI}…
The paper presents a mean field theory of electrolyte solutions, extending the classical Debye-H\"{u}ckel-Onsager theory to provide a detailed description of the electrical conductivity in strong electrolyte solutions. The theory…
We set up a general framework for systematically building and classifying, in the linear regime, causal and stable dissipative hydrodynamic theories that, alongside with the usual hydrodynamic modes, also allow for an arbitrary number of…
A system modeling the electrophoretic motion of a charged rigid macromolecule immersed in a incompressible ionized fluid is considered. The ionic concentration is governing by the Nernst-Planck equation coupled with the Poisson equation for…
Current research presents an innovative model of half-space plasmon excitations for electron gas of arbitrary degeneracy in an ambient jellium-like positive background . The linearized Schr\"{o}dinger-Poisson system is used to derive…
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…
We show the continuity of the flow map for quasilinear symmetric hyperbolic systems with general right--hand sides in different functional setting, including weighted Sobolev spaces $H_{s,\delta}$. An essential tool to achieve the…
Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects in a way that total charge and energy are conserved. The…
The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to…
Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the…
We consider one-dimensional, locally finite interacting particle systems with two conservation laws. The models have a family of stationary measures with product structure and we assume the existence of a uniform bound on the inverse of the…
Analogue systems are a powerful instrument to investigate and understand in a controlled setting many general-relativistic effects. Here, we focus on superradiant-triggered instabilities and quasi-normal modes. We consider a compressible…
We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in…
The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…
The sensitivity of charge, heat, or momentum transport to the sample geometry is a hallmark of viscous electron flow. Therefore, hydrodynamic electronics requires the detailed understanding of electron flow in finite geometries. The…
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…
We introduce a diffuse interface model for the phenomenon of electrowetting on dielectric and present an analysis of the arising system of equations. Moreover, we study discretization techniques for the problem. The model takes into account…
A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open…
A diffusive model of osmosis is presented that explains currently available experimental data. It makes predictions that distinguish it from the traditional convective flow model of osmosis, some of which have already been confirmed…