scholarly journals On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

2003 ◽  
Vol 282 (1) ◽  
pp. 212-231 ◽  
Author(s):  
Guy Bayada ◽  
Mahdi Boukrouche
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Reynolds Equation ◽  
Stokes System ◽  
A Free Boundary Problem

scholarly journals On the existence of two stationary solutions for a free boundary problem describing cell motility

2016 ◽  
Vol 47 (1) ◽  
Author(s):  
Harunori Monobe
Keyword(s):  
Maximum Principle ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Cell Motility ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Stationary Solutions ◽  
Weak Maximum Principle ◽  
The Mean ◽  
A Free Boundary Problem

This paper is concerned with the existence of stationary solutions for a free boundary problem related to cell motility. In recent years, the author and Ninomiya \cite{monobe_ninomiya} showed that there exist at least two stationary solutions with disk-shaped domains in isotropic boundary conditions. In this paper, it will be shown that there exist exactly two stationary solutions for the free boundary problem under the same boundary conditions. The proof is based on the weak maximum principle and the mean-valued theorem.

scholarly journals Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abdelkader Saadallah ◽  
Nadhir Chougui ◽  
Fares Yazid ◽  
Mohamed Abdalla ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Reynolds Equation ◽  
Limit Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Thin Domain

In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the velocity and the pressure of the fluid, and we obtain the limit problem and the specific Reynolds equation.

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.

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