Related papers: On a drift-diffusion system for semiconductor devi…
We consider an abstract first order evolution equation in a Hilbert space in which the linear part is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the…
We are concerned with large-time behaviors of solutions for Vlasov--Navier--Stokes equations in two dimensions and Vlasov-Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the…
The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. In this work, we propose a macroscopic mathematical…
We investigate a recombination-drift-diffusion model coupled to Poisson's equation modelling the transport of charge within certain types of semiconductors. In more detail, we study a two-level system for electrons and holes endowed with an…
We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier--Stokes equations. The leading-order term is the well-known diffusion wave and the higher-order terms are newly introduced…
We study the full probability distribution of the charge transmitted through a mesoscopic diffusive conductor during a measurement time T. We have considered a semi-classical model, with an exclusion principle in a discretized…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
A theory of nonlinear signal propagation in multi-span wavelength division multiplexed coherent transmission systems that employ the semiconductor optical amplifier as in-line amplifiers is presented for the first time. The rigorous…
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…
Under specific experimental circumstances, sputter erosion on semiconductor materials exhibits highly ordered hexagonal dot-like nanostructures. In a recent attempt to theoretically understand this pattern forming process, Facsko et al.…
We consider the Vlasov--Poisson system in a $C^3$ convex domain $D$ with a perfectly conducting wall. We introduce the asymptotic domain $D_{\infty}$ for the domain $D$. Then under acceptable assumptions on $D$, we show that for localized…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…
Equation of long-range particle drift and diffusion on three-dimensional physical lattice is suggested. This equation can be considered as a lattice analogof space-fractional Fokker-Planck equation for continuum. The lattice approach gives…
We apply the Wigner function formalism to derive drift-diffusion transport equations for spin-polarized electrons in a III-V semiconductor single quantum well. Electron spin dynamics is controlled by the linear in momentum spin-orbit…
The electro-diffusion model, which arises in electrohydrodynamics, is a coupling between the Nernst-Planck-Poisson system and the incompressible Navier-Stokes equations. For the generally smooth doping profile, the quasineutral limit…
We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…
We investigate the dissipativity properties of a class of scalar second order parabolic partial differential equations with time-dependent coefficients. We provide explicit condition on the drift term which ensure that the relative entropy…
We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
We study a class of McKean--Vlasov Stochastic Differential Equations (MV-SDEs) with drifts and diffusions having super-linear growth in measure and space -- the maps have general polynomial form but also satisfy a certain monotonicity…