scholarly journals Traveling wave solutions with convex domains for a free boundary problem

2017 ◽  
Vol 37 (2) ◽  
pp. 905-914 ◽  
Author(s):  
Harunori Monobe ◽  
◽  
Hirokazu Ninomiya ◽  
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Convex Domains ◽  
Wave Solutions ◽  
A Free Boundary Problem

scholarly journals Self polarization and traveling wave in a model for cell crawling migration

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Alessandro Cucchi ◽  
Antoine Mellet ◽  
Nicolas Meunier
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Constructive Method ◽  
Graph Analysis ◽  
Bifurcation Method ◽  
Wave Solutions ◽  
Cell Crawling

<p style='text-indent:20px;'>In this paper, we prove the existence of traveling wave solutions for an incompressible Darcy's free boundary problem recently introduced in [<xref ref-type="bibr" rid="b6">6</xref>] to describe cell motility. This free boundary problem involves a nonlinear destabilizing term in the boundary condition which describes the active character of the cell cytoskeleton. By using two different methods, a constructive method via a graph analysis and a local bifurcation method, we prove that traveling wave solutions exist when the destabilizing term is strong enough.</p>

Travelling wave solutions of a reaction—infiltration problem and a related free boundary problem

1994 ◽  
Vol 5 (3) ◽  
pp. 255-265 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Elena Comparini ◽  
Riccardo Ricci
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Suitable Norm ◽  
Formal Limit ◽  
A Free Boundary Problem

We consider travelling wave solutions of a reaction–diffusion system arising in a model for infiltration with changing porosity due to reaction. We show that the travelling wave solution exists, and is unique modulo translations. A small parameter ε appears in this problem. The formal limit as ε → 0 is a free boundary problem. We show that the solution for ε > 0 tends, in a suitable norm, to the solution of the formal limit.

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.

Sign in / Sign up

Export Citation Format

Share Document