On a fractional thin film equation

关于双退化六阶薄膜方程的源型解和Cauchy问题I。局部振荡性质

On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation I. Local oscillatory properties

研究了双非线性六阶抛物薄膜方程源型解的局部振动性及其它性质。

薄膜方程非对称行波解的存在性和行为

Existence and behavior of asymmetric traveling wave solutions to thin film equation

我们证明了在液-固界面上具有Navier滑移条件的薄膜方程行波解的存在性和唯一性。我们得到明确的上下上界的解决方案和绝对误差估计的近似的解决方案的薄膜方程的行波解。

Justification of a nonlinear sixth-order thin-film equation as the reduced model for a fluid -- structure interaction problem

Starting from a nonlinear 2D/1D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic structure, on the vanishing limit of the relative fluid thickness, we rigorously derive a sixth-order thin-film equation describing the dynamics of vertical displacements of the structure. The procedure is essentially based on quantitative energy estimates, quantified in terms of the relative fluid thickness, and a uniform no-contact result between the structure and the solid substrate. The sixth-order thin-film equation is justified in the sense of strong convergence …

二维情况下薄膜方程弱解的Hölder连续性

Hölder continuity of weak solutions to the thin-film equation in $d=2$

本文研究了二维情况下薄膜方程弱解的Hölder连续性，通过孔填充技术克服了四阶偏微分方程的退化抛物性挑战。

Some thin film models based on Shikhmurzaev's approach

We derive several lubrication approximation models, using Shikhmurzaev's approach to the contact line problem, obtained in \cite{GNV}. The first two lubrication models describe thin film flow of incompressible fluids on solid substrates, based on different orders of magnitude of the slip length parameter. The third lubrication model describes a meniscus formation where a wedge-shaped solid immerses in a thin film of fluid.

具有非线性表面张力项的薄膜方程

On the thin-film equation with nonlinear surface tension term

本文考虑一维空间中具有非线性表面张力项的薄膜方程。依靠相应的能量和熵估计，我们证明了弱解的存在性以及非负性结果。

分数Sobolev空间在低积分性 regime 下的渐进行为

Asymptotic analysis of fractional Sobolev spaces on thin films in the low-integrability regime

研究薄片上分数Sobolev空间的渐进行为，证明其趋近于H^{s+1/2}(ω)空间，通过维度缩减收敛概念和适当缩放的Gagliardo半范数定义等 coercive 函数。

含可溶性表面活性剂和重力的薄膜方程：建模和定态稳定性

Thin Film Equations with Soluble Surfactant and Gravity: Modeling and Stability of Steady States

被认为是一个薄膜上的水平固体基板和涂有可溶性表面活性剂。当考虑重力时，使用润滑近似推导出用于膜高度和表面活性剂在表面上和在体中的浓度的控制退化抛物方程。结果表明，定态是渐近稳定的。

斜面流动薄膜近似的数学证明

A Mathematical Justification of a Thin Film Approximation for the Flow down an Inclined Plane

本文考虑薄膜在重力和表面张力的影响下沿斜面流下的二维运动。为了研究这种流动的稳定性，我们经常使用薄膜近似，这是一个近似通过微扰展开相对于膜的纵横比。近似方程的著名例子有Burgers方程、Kuramoto-Sivashinsky方程、KdV-Burgers方程、KdV-Kuramoto-Sivashinsky方程等.本文通过建立Navier-斯托克斯方程的解与近似方程的解之间的误差估计，给出了薄膜近似的严格数学证明.

薄膜区粘性不可压缩流体沿斜面流动的一致估计

Uniform Estimates for the Flow of a Viscous Incompressible Fluid down an Inclined Plane in the Thin Film Regime

本文考虑薄膜在重力和表面张力的影响下沿斜面流下的二维运动。为了研究这种流动的稳定性，很难直接处理Navier-斯托克斯方程，因此通常采用薄膜近似。它是在薄膜状态下通过微扰展开相对于膜的纵横比$δ$获得的近似值$δ\ll1$。我们的目的是通过建立Navier-斯托克斯方程的解与近似方程的解之间的误差估计，给出薄膜近似的数学上严格的理由。为此，本文在适当的假设下，得到了斯托克斯方程关于$δ$的解的一致估计。

一类四阶薄膜方程全局和“Blow-up”模式的局部分歧-分支分析

Local Bifurcation-Branching Analysis of Global and "Blow-up" Patterns for a Fourth-Order Thin Film Equation

证明了$R^N$中的拟线性四阶薄膜方程存在无穷可数族的整体解和爆破相似解，这些解源于相应的线性非自伴算子的本征函数的极限.

双退化迁移率薄膜方程间断数据的自相似坍塌

On self-similar collapse of discontinuous data for thin film equations with doubly degenerate mobility

证明了薄膜方程在+1和-1处退化的具有符号型间断数据的Riemann型问题存在自相似解。FBP和柯西问题（界面附近的振荡解）的设置都考虑在内。

一类四阶薄膜方程可数族整体相似解的分支分析

Branching analysis of a countable family of global similarity solutions of a fourth-order thin film equation

我们证明了四阶拟线性薄膜方程的整体解的各种渐近性质可以通过从线性双调和方程的相应解分支来描述。这包括自相似解的可数族和其他方面。

Asymptotic analysis for a second order curved thin film

We consider a second order thin curved film whose behavior is governed by an energy made up of a first order nonlinear part depending on the gradient of the deformation augmented by a quadratic second order part depending on the tensor of second derivatives of the deformation. We carry out a 3D-2D analysis through an asymptotic expansion in powers of the thickness of the film as it tends to zero.

强磁场中薄膜超导体的奇异极限--薄膜的Maan场模型

Singular Limits for Thin Film Superconductors in Strong Magnetic Fields - Maan Field Model for Thin Films

本文研究了具有薄膜几何形状的超导体在恒定外磁场中的三维Ginzburg-Landau泛函的奇异极限。超导畴具有$\eps>0$尺度上的特征厚度，我们认为同时限制为厚度$\eps\rightarrow 0$和Ginzburg-Landau参数$κ\rightarrow\infty$。我们假设所施加的场在其与膜域相切的分量中是强的（量级为$\eps^{-1}$），并且在其对$κ$的依赖性中是$\logκ$级。我们证明，金斯堡-朗道能量$Γ$ -收敛到一个能量与两个障碍的问题，提出的平面域上支持的薄膜。无论限度中$\eps$和$κ$之间的关系如何，均获得相同的限度。两个说明性的例子，其中每一个演示了如何的曲率的电影可以诱导存在的两个（积极取向）的旋涡和（消极取向）的反涡共存的能量的全局极小。

A note on the homogenization of incommensurate thin films

Dimension-reduction homogenization results for thin films have been obtained under hypotheses of periodicity or almost-periodicity of the energies in the directions of the mid-plane of the film. In this note we consider thin films, obtained as sections of a periodic medium with a mid-plane that may be incommensurate; that is, not containing periods other than $0$. A geometric almost-periodicity argument similar to the cut-and-project argument used for quasicrystals allows to prove a general homogenization result.