Related papers: Well-posedness for a molecular beam epitaxy model

The energetically driven Ehrlich-Schwoebel (ES) barrier had been generally accepted as the primary cause of the growth instability in the form of quasi-regular mound-like structures observed on the surface of thin film grown via molecular…

The naturally existing chalcogenide Bi2Se3 is topologically nontrivial due to the band inversion caused by strong spin-orbit coupling inside the bulk of the material. The surface states are spin polarized, protected by the time-inversion…

We report the structural and optical properties of molecular beam epitaxy (MBE) grown 2-dimensional (2D) material molybdenum diselenide (MoSe2) on graphite, CaF2 and epitaxial graphene. Extensive characterizations reveal that 2H- MoSe2…

We study local existence and uniqueness for a surface growth model with space-time white noise in 2D. Unfortunately, the direct fixed-point argument for mild solutions fails here, as we do not have sufficient regularity for the stochastic…

Epitaxial films of NdFeAsO were grown on GaAs substrates by molecular beam epitaxy (MBE). All elements including oxygen were supplied from solid sources using Knudsen cells. The x-ray diffraction pattern of the film prepared with the…

Molecular beam epitaxy enables the growth of thin film materials with novel properties and functionalities. Typically, the lattice constants of films and substrates are designed to match to minimise disorders and strains. However,…

In this paper, we mainly investigate the Cauchy problem of the non-viscous MHD equations with magnetic diffusion. We first establish the local well-posedness (existence,~uniqueness and continuous dependence) with initial data $(u_0,b_0)$ in…

The lattice mismatch between interesting 2D materials and commonly available 3D substrates is one of the obstacles in the epitaxial growth of monolithic 2D/3D heterostructures, but a number of 2D materials have not yet been considered for…

The growth of wafer-scale van der Waals (vdW) thin films and heterostructures by molecular beam epitaxy (MBE) is important for future applications in quantum technologies, next generation optoelectronic devices, and fundamental physics…

Molecular beam epitaxy is one of the highest quality growth methods, capable of achieving theoretical material property limits and unprecedented device performance. However, such ultimate quality usually comes at the cost of painstaking…

We study solutions of a Euclidean weighted porous medium equation when the weight behaves at spacial infinity like $|x|^{-\gamma}$, for $\gamma\in [0,2)$, and is allowed to be singular at the origin. In particular we show local-in-time…

We report the molecular beam epitaxy of Bi_1-xSb_x thin films ($0 \leq x \leq 1$) on (0001) sapphire substrates using a thin (Bi,Sb)$_2$Te$_3$ buffer layer. Characterization of the films using reflection high energy diffraction, x-ray…

In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…

This paper concerns the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane $\mathbb{R}^2$ with zero density at infinity. By spatial weighted energy method, we derive the local…

We consider the Cauchy problem for strictly hyperbolic $m$-th order partial differential equations with coefficients low-regular in time and smooth in space. It is well-known that the problem is $L^2$ well-posed in the case of Lipschitz…

Materials with perpendicular magnetic anisotropy (PMA) effect with high Curie temperature ($T_C$) is essential in applications. In this work, $Cr_2Te_3$ thin films showing PMA with $T_C$ ranging from 165 K to 295 K were successfully grown…

We investigate the well-posedness of the fast diffusion equation (FDE) in a wide class of noncompact Riemannian manifolds. Existence and uniqueness of solutions for globally integrable initial data was established in [5]. However, in the…

In the paper, we consider the Cauchy problem of the non-resistive MHD equations in homogeneous Besov spaces. We prove the local existence and uniqueness of the solution to the non-resistive MHD equations by using the iterative scheme and…

In this paper we study both the Cauchy problem and the initial boundary value problem for the equation $\partial_tu+\mbox{div}\left(\nabla\Delta u-{\bf g}(\nabla u)\right)=0$. This equation has been proposed as a continuum model for kinetic…

This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Magnetohydrodynamic (MHD) equations with vacuum as far field density. We establish the global existence and uniqueness of strong solutions to…