Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid

1992 ◽  
pp. 30-55 ◽  
Author(s):  
V. A. Solonnikov ◽  
A. Tani
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Equations Of Motion ◽  
Barotropic Liquid

Meniscus growth during the wiping stage of intaglio (gravure) printing

2016 ◽  
Vol 807 ◽  
pp. 419-440
Author(s):  
Umut Ceyhan ◽  
S. J. S. Morris
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Upper Bound ◽  
Capillary Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Gravure Printing ◽  
Tip Radius

During intaglio (gravure) printing, a blade wipes excess ink from the engraved plate with the object of leaving ink-filled cells defining the image to be printed. That objective is not completely attained. Capillarity draws some ink from the cell into a meniscus connecting the blade to the substrate, and the continuing motion of the engraved plate smears that ink over its surface. By examining the limit of vanishing capillary number ($Ca$, based on substrate speed), we reduce the problem of determining smear volume to one of hydrostatics. Using numerical solutions of the corresponding free-boundary problem for the Stokes equations of motion, we show that the hydrostatic theory provides an upper bound to smear volume for finite $Ca$. The theory explains why polishing to reduce the tip radius of the blade is an effective way to control smearing.

Uniqueness of solution to a free boundary problem from combustion with transport

MAT Serie A ◽  
2001 ◽  
Vol 5 ◽  
pp. 37-41
Author(s):  
Claudia Lederman ◽  
Juan Luis Vázquez ◽  
Noemí Wolanski
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Uniqueness Of Solution ◽  
A Free Boundary Problem

EXISTENCE OF PERIODIC SOLUTIONS FOR A FREE BOUNDARY PROBLEM OF HYPERBOLIC TYPE

2008 ◽  
Vol 05 (04) ◽  
pp. 785-806
Author(s):  
KAZUAKI NAKANE ◽  
TOMOKO SHINOHARA
Keyword(s):  
Mathematical Model ◽  
Free Boundary ◽  
Hyperbolic Equation ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Physical Phenomenon ◽  
Hyperbolic Type ◽  
Existence Of Periodic Solutions ◽  
A Free Boundary Problem ◽  
Thin Tape

A free boundary problem that arises from the physical phenomenon of "peeling a thin tape from a domain" is treated. In this phenomenon, the movement of the tape is governed by a hyperbolic equation and is affected by the peeling front. We are interested in the behavior of the peeling front, especially, the phenomenon of self-excitation vibration. In the present paper, a mathematical model of this phenomenon is proposed. The cause of this vibration is discussed in terms of adhesion.

An evolutional free-boundary problem of a reaction–diffusion–advection system

2017 ◽  
Vol 147 (3) ◽  
pp. 615-648 ◽  
Author(s):  
Ling Zhou ◽  
Shan Zhang ◽  
Zuhan Liu
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Ecological Model ◽  
Reaction Diffusion ◽  
Spreading Speed ◽  
Heterogeneous Environment ◽  
Long Run ◽  
Strong Competition ◽  
Asymptotic Spreading

In this paper we consider a system of reaction–diffusion–advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. The evolution of the free-boundary problem is discussed, which is an extension of the results of Du and Lin (Discrete Contin. Dynam. Syst. B19 (2014), 3105–3132). Precisely, when u is an inferior competitor, we prove that (u, v) → (0, V) as t→∞. When u is a superior competitor, we prove that a spreading–vanishing dichotomy holds, namely, as t→∞, either h(t)→∞ and (u, v) → (U, 0), or limt→∞h(t) < ∞ and (u, v) → (0, V). Moreover, in a weak competition case, we prove that two competing species coexist in the long run, while in a strong competition case, two species spatially segregate as the competition rates become large. Furthermore, when spreading occurs, we obtain some rough estimates of the asymptotic spreading speed.

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