scholarly journals Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations

2021 ◽  
Vol 299 ◽  
pp. 542-601
Author(s):  
Chengchun Hao ◽  
Tao Luo
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Well Posedness ◽  
Magnetohydrodynamics Equations ◽  
Ideal Magnetohydrodynamics

Gelification and mass transport in a static non-isothermal waxy solution

2009 ◽  
Vol 20 (1) ◽  
pp. 93-122 ◽  
Author(s):  
A. FASANO ◽  
L. FUSI ◽  
J. R. OCKENDON ◽  
M. PRIMICERIO
Keyword(s):  
Free Boundary ◽  
Mass Transport ◽  
Boundary Problem ◽  
Cloud Point ◽  
Free Boundary Problem ◽  
Mathematical Problem ◽  
Well Posedness ◽  
Dimensional Model ◽  
One Dimensional ◽  
A Free Boundary Problem

We consider a solution of a mono-component oil and wax. The latter is dissolved in the oil if the temperature is above the so-called cloud point (which depends on the concentration) and it segregates in the form of solid crystals if temperature is below the cloud point. As the solid fraction of wax increases, the diffusivity of liquid wax in the oil decreases (gelification), eventually vanishing. We study a one-dimensional model where temperature is initially above the cloud point and then it is lowered to induce diffusion and gelification. We formulate the relevant mathematical problem (a free boundary problem), studying its well-posedness and showing some qualitative results.

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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