Related papers: Degenerate drift-diffusion systems for memristors
This article studies, both theoretically and numerically, a nonlinear drift-diffusion equation describing a gas of fermions in the zero-temperature limit. The equation is considered on a bounded domain whose boundary is divided into an…
We revisit the homogenization problem for the Poisson equation in periodically perforated domains with zero Neumann data at the boundary of the holes and prescribed Dirichlet data at the outer boundary. It is known that, if the periodicity…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the $L^q$-energy inequality and speed estimate in Wasserstein spaces under some integrability conditions on the drift term.…
We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other applications, in the context of semiconductor modeling for perovskite…
In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…
Revisiting charge transport in degenerate hopping systems we present a modification to the drift diffusion equation where instead of employing the generalized Einstein relation we add an energy flux term thus solving several…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
The purpose of this paper is to examine stochastic Markovian models for circuits in phase space for which the drift term is equivalent to the standard circuit equations. In particular we include dissipative components corresponding to both…
In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D) materials have demonstrated promising potential for…
We prove existence of global weak solutions for the Nernst-Planck-Poisson problem which describes the evolution of concentrations of charged species $X_1, ..., X_P$ subject to Fickian diffusion and chemical reactions in the presence of an…
The flow of ions through permeable channels causes voltage drop in physiological nanodomains such as synapses, dendrites and dendritic spines, and other protrusions. How the voltage changes around channels in these nanodomains has remained…
We consider charge transport in nanopores where the dielectric constant inside the nanopore is much greater than in the surrounding material, so that the flux of the electric fields due to the charges is almost entirely confined to the…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…
This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally,…
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…
A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…
Time-dependent density functional theory is extended to include dissipative systems evolving under a master equation, providing a Hamiltonian treatment for molecular electronics. For weak electric fields, the isothermal conductivity is…