The porous medium equation as a singular limit of the thin film Muskat problem

Asymptotics for the Spectrum of a Thin Film Equation in a Singular Limit

In this paper the linear stability properties of the steady states of a no-slip lubrication equation are studied. The steady states are configurations of droplets and arise during the late-phase dewetting process under the influence of both destabilizing van der Waals and stabilizing Born intermolecular forces, which in turn give rise to the minimum thickness ε of the remaining film connecting ...

the problem of divine hiddenness

این رساله به مساله احتجاب الهی و مشکلات برهان مبتنی بر این مساله میپردازد. مساله احتجاب الهی مساله ای به قدمت ادیان است که به طور خاصی در مورد ادیان ابراهیمی اهمیت پیدا میکند. در ادیان ابراهیمی با توجه به تعالی خداوند و در عین حال خالقیت و حضور او و سخن گفتن و ارتباط شهودی او با بعضی از انسانهای ساکن زمین مساله ای پدید میاید با پرسشهایی از قبیل اینکه چرا ارتباط مستقیم ویا حداقل ارتباط وافی به ب...

Porous media: the Muskat problem in 3D

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.

[hal-00636647, v1] A gradient flow approach to a thin film approximation of the Muskat problem

Abstract. A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two ...

A gradient flow approach to a thin film approximation of the Muskat problem