Free boundary problems in the theory of fluid flow through porous media: Existence and uniqueness theorems

1973 ◽  
Vol 97 (1) ◽  
pp. 1-82 ◽  
Author(s):  
C. Baiocchi ◽  
V. Comincioli ◽  
E. Magenes ◽  
G. A. Pozzi
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Free Boundary Problems ◽  
Uniqueness Theorems ◽  
Flow Through Porous Media ◽  
Boundary Problems ◽  
Existence And Uniqueness Theorems ◽  
Flow Through

Free boundary problems in the theory of fluid flow through porous media: A numerical approach

CALCOLO ◽  
1973 ◽  
Vol 10 (1) ◽  
pp. 1-85 ◽  
Author(s):  
C. Baiocchi ◽  
V. Comincioli ◽  
L. Guerri ◽  
G. Volpi
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Free Boundary ◽  
Free Boundary Problems ◽  
Numerical Approach ◽  
Flow Through Porous Media ◽  
Boundary Problems ◽  
Flow Through

scholarly journals Free boundary problems in biology

2015 ◽  
Vol 373 (2050) ◽  
pp. 20140368 ◽  
Author(s):  
Avner Friedman
Keyword(s):  
Mathematical Model ◽  
Wound Healing ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Free Boundary Problems ◽  
Uniqueness Theorems ◽  
Biological Processes ◽  
Boundary Problems ◽  
Mathematical Problems ◽  
The Mathematical Model

In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state mathematical results, including existence and uniqueness theorems, stability and asymptotic limits, and the behaviour of the free boundary. I also suggest, for each of the topics, open mathematical problems.

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