Related papers: Degenerate drift-diffusion systems for memristors
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
We analyze numerically and analytically the non linear transport properties of a drift-diffusion equation in presence of a magnetic field and of a disorder potential. For a wide range of parameters this model exhibits a plateau where the…
An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations for the ion concentrations include drift terms involving…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly…
The operation of a novel nonvolatile memory device based on a conductive ferroelectric/non-ferroelectric thin film multilayer stack is simulated numerically. The simulation involves the self-consistent steady state solution of Poisson's…
The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift-diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and…
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…
We regard drift-diffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
This paper presents an improved version of the previously proposed self-consistent drift-diffusion-reaction model correcting for non-physical behavior at longer time scales. To this end a novel boundary condition is employed that takes into…
This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a…
We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular…
We propose in this paper to derive and analyze a self-consistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultra-scaled confined structure, taking in…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
We are concerned in this paper with the degenerate fractional diffusion advection equations posed in bounded domains. Due to a suitable formulation, we show the existence of weak entropy solutions for measurable and bounded initial and…
The peculiarities of electric current in semiconductors with nonuniform distribution of charge carriers are studied. The semiclassical drift-diffusion equations consisting of the continuity equations and the Poisson equation are solved…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
A Wigner-Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are supposed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron-electron…