A free boundary problem for a reaction-diffusion system with nonlinear memory

2013 ◽  
Vol 65 (3) ◽  
pp. 521-530 ◽  
Author(s):  
Zhigui Lin ◽  
Zhi Ling ◽  
Michael Pedersen
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Nonlinear Memory ◽  
A Free Boundary Problem

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.

A free boundary problem arising in some reacting–diffusing system

1991 ◽  
Vol 118 (3-4) ◽  
pp. 355-378 ◽  
Author(s):  
D. Hilhorst ◽  
Y. Nishiura ◽  
M. Mimura
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Finite Dimension ◽  
Reaction Diffusion ◽  
Diffusion Limit ◽  
Well Posedness ◽  
One Dimensional ◽  
A Free Boundary Problem ◽  
Large Diffusion

SynopsisWe prove the well-posedness for a one-dimensional free boundary problem arising from some reaction diffusion system. The interfacial point hits a boundary point in finite time or remains inside for all time. In the large diffusion limit, the system is reduced to ordinary differential equations of finite dimension.

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