Related papers: Mathematical analysis of a partial differential eq…

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…

Polytetrafluoroethylene (PTFE) is an excellent diffuse reflector widely used in light collection systems for particle physics experiments. However, the reflectance of PTFE is a function of its thickness. In this work, we investigate this…

This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the…

In the 2nd version of this note we introduce the notion of viscosity solution for a type of fully nonlinear parabolic path-dependent partial differential equations (P-PDE). We then prove the comparison theorem (or maximum principle) of this…

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…

In this paper, we consider the problem of obtaining rational decay for a particular time-evolving fluid-structure model, the type of which has been considered in Chueshov and Ryzhkova (2013). In particular, this partial differential…

We propose a sharp-interface model for solid-state dewetting of thin films with wetting potential, where the wetting effect is incorporated through a thickness-dependent surface energy. The model is governed by surface diffusion together…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…

Diffusion-based models have demonstrated impressive accuracy and generalization in solving partial differential equations (PDEs). However, they still face significant limitations, such as high sampling costs and insufficient physical…

The film thickness dependence of crystal growth is investigated for isotactic polystyrene (it-PS) in thin films, the thickness of which is from 20nm down to 4nm. The single crystals of it-PS grown at 180 in the ultrathin films show the…

We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\log n)$…

The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated,…

The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that…

The stability of thin liquid coatings is of fundamental interest in every- day life. Homogeneous and non-volatile liquid coatings may dewet either by heterogeneous nucleation, thermal nucleation, or spinodal dewetting. Wetting and dewetting…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic…

We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of spontaneous curvature effects and for open surfaces with…

We present a novel approach that redefines the traditional interpretation of explicit and implicit discretization methods for solving a general class of advection-diffusion equations (ADEs) featuring nonlinear advection, diffusion…

The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…