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

We study a nonlinear porous medium type equation involving the infinity Laplacian operator. We first consider the problem posed on a bounded domain and prove existence of maximal nonnegative viscosity solutions. Uniqueness is obtained for…

The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or…

We demonstrate the making of BaZrS3 thin films by molecular beam epitaxy (MBE). BaZrS3 forms in the orthorhombic distorted-perovskite structure with corner-sharing ZrS6 octahedra. The single-step MBE process results in films smooth on the…

In any number of space variables, we study the Cauchy problem related to the thin-film equation in the simplest case of a linearly degenerate mobility. This equation, derived from a lubrication approximation, also models the surface tension…

This paper introduces a growth method---suboxide molecular-beam epitaxy (S-MBE)---which enables the growth of Ga2O3 and related materials at growth rates exceeding 1 micrometer per hours with excellent crystallinity in an…

We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the…

This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of…

In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\mathcal{O} \subset \mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective…

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth…

In this paper, we prove the existence of a unique maximal local strong solutions to a stochastic system for both 2D and 3D penalised nematic liquid crystals driven by multiplicative Gaussian noise. In the 2D case, we show that this solution…

In this paper we study the Gevrey regularity for the weak solutions to the Cauchy problem of the non-cutoff spatially homogeneous Botlzmann equation for the Maxwellian molecules model with the singularity exponent $s\in (0,1)$. We establish…

For a real-valued one dimensional diffusive strict local martingale,, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local H\"older condition. Under the weaker Engelbert-Schmidt…

In this work we address some questions concerning the Cauchy problem for a generalized nonlinear heat equations considering as functional framework the variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$. More precisely, by mixing some…

In this paper we prove several results related to the existence and uniqueness of solution to coupled highly nonlinear stochastic partial differential equations (PDEs). These equations are motivated by the dynamics of nematic liquid…

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…

The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The…

In this work, we show the heteroepitaxial growth of single-crystalline bixbyite (In$_{1-x}$Ga$_x$)$_2$O$_3$ films on (111)-oriented yttria-stabilized zirconia substrates using plasma-assisted molecular beam epitaxy under various growth…

Transition metal dichalcogenides (TMDCs), together with other two-dimensional (2D) materials have attracted great interest due to the unique optical and electrical properties of atomically thin layers. In order to fulfill their potential,…

We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. We…