相关论文: The Variable Coefficient Hele-Shaw Problem, Integr…

This article is devoted to the study of the Hele-Shaw equation. We introduce an approach inspired by the water-wave theory. Starting from a reduction to the boundary, introducing the Dirichlet to Neumann operator and exploiting various…

We introduce and investigate a generalization of the Hele-Shaw flow with injection where several droplets compete for space as they try to expand due to internal pressure while still preserving their topology. Droplets are described by…

In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are governed by elliptic equations with constant coefficients. This…

We present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the…

Kow, Larson, Salo and Shahgholian recently initiated the study of quadrature domains for the Helmholtz equation and developed an associated theory of partial balayage of measures. The present paper offers an alternative approach to partial…

The present paper deals with the interior solid-fluid interaction problem in harmonic regime with randomly perturbed boundaries. Analysis of the shape derivative and shape Hessian of vector- and tensor-valued functions is provided. Moments…

Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast c=(mu_1-mu_2)/(mu_1+mu_2), in a model porous medium defined as a Hele-Shaw cell with random gap b_0+delta b. Fluctuations…

We study a diffuse interface model describing the motion of two viscous fluids driven by the surface tension in a Hele-Shaw cell. The full system consists of the Cahn-Hilliard equation coupled with the Darcy's law. We address the physically…

We consider self-similar potential flow for compressible gas with polytropic pressure law. Self-similar solutions arise as large-time asymptotes of general solutions, and as exact solutions of many important special cases like Mach…

Various thermodynamical phenomena have occurred with change of pressure and temperature, volume. We can choose these parameters but not these constraints, in order to need the thermodynamics with physical properties in the fields of various…

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to…

We discuss conjectural scaling limits of discrete 2-dimensional aggregation models conditioned on a semi-axis considered by Levine and Peres in arXiv:0712.3378. These are certain problems about Hele-Show flows. We study moment properties of…

This paper is concerned with a rigorous convergence analysis of a fully discrete Lagrangian scheme for the Hele-Shaw flow, which is the fourth order thin-film equation with linear mobility in one space dimension. The discretization is based…

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…

A Hele-Shaw cell is a device used to study fluid flow between two parallel plates separated by a small gap. The governing equation of flow within a Hele-Shaw cell is Darcy's law, which also describes flow through a porous medium. In this…

It is known that any subharmonic quadrature domain in two dimensions satisfies a natural inner ball condition, in other words there is a specific upper bound on the curvature of the boundary. This result directly applies to free boundaries…

We present a new connection between the Hele-Shaw flow, also known as two-dimensional (2D) Laplacian growth, and the theory of holomorphic discs with boundary contained in a totally real submanifold. Using this we prove short time existence…

In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…

We consider the numerical integration of moving boundary problems with the curve-shortening property, such as the mean curvature flow and Hele-Shaw flow. We propose a fully discrete curve-shortening polygonal evolution law. The proposed…