scholarly journals Evolution of a Geothermal System with Fluid Re-Injection

2020 ◽  
Vol 10 (21) ◽  
pp. 7561
Author(s):  
Angiolo Farina ◽  
Antonio Fasano ◽  
Mario Primicerio ◽  
Fabio Rosso
Keyword(s):  
Mathematical Model ◽  
Free Boundary ◽  
Stationary Solutions ◽  
Geothermal Field ◽  
Geothermal System ◽  
Stable States ◽  
General Mathematical Model ◽  
The One ◽  
A Free Boundary Problem ◽  
Natural Recharge

In this paper, we study the stationary configurations of a vapor-dominated geothermal system. We propose a general mathematical model, which turns out to be a free boundary problem, and we focus on the stationary solutions. The analysis, developed considering the data of the geothermal field in Larderello, Tuscany (Italy), shows that steady-stable states may exist both when the re-injection takes place in depth and when the natural recharge is distributed both in the area occupied by vapor and in the one occupied by liquid.

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.

scholarly journals Stability of Solutions to a Free Boundary Problem for Tumor Growth

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Shihe Xu
Keyword(s):  
Free Boundary ◽  
Tumor Growth ◽  
Asymptotic Behaviour ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Stationary Solutions ◽  
Steady Solution ◽  
Stability Of Solutions ◽  
Steady Solutions ◽  
A Free Boundary Problem

We study the asymptotic behaviour of quasi-stationary solutions of a free boundary problem which had been discussed by Bueno (2005). Using a simpler method we prove that the quasi-steady solutions of the problem converge uniformly to the unique nontrivial steady solution.

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