Phase transitions in a model porous medium

1993 ◽  
Vol 48 (5) ◽  
pp. 3124-3129 ◽  
Author(s):  
Michael R. Swift ◽  
E. Cheng ◽  
Milton W. Cole ◽  
Jayanth R. Banavar
2017 ◽  
Vol 58 (2) ◽  
pp. 271-274 ◽  
Author(s):  
R. F. Sharafutdinov ◽  
A. S. Bochkov ◽  
A. M. Sharipov ◽  
A. A. Sadretdinov

1994 ◽  
Vol 29 (6) ◽  
pp. 834-837
Author(s):  
R. A. Valiullin ◽  
A. Sh. Ramazanov ◽  
R. F. Sharafutdinov

1996 ◽  
Vol 53 (1) ◽  
pp. 148-158 ◽  
Author(s):  
T. MacFarland ◽  
G. T. Barkema ◽  
J. F. Marko

2021 ◽  
Vol 382 (1) ◽  
pp. 485-545
Author(s):  
José A. Carrillo ◽  
Rishabh S. Gvalani

AbstractWe are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $$1< m < \infty $$ 1 < m < ∞ . We first prove the existence of possibly infinitely many bifurcations from the spatially homogeneous steady state. We then focus our attention on the associated free energy, proving existence of minimisers and even uniqueness for sufficiently weak interactions. In the absence of uniqueness, we show that the system exhibits phase transitions: we classify values of m and interaction potentials W for which these phase transitions are continuous or discontinuous. Finally, we comment on the limit $$m \rightarrow \infty $$ m → ∞ and the influence that the presence of a phase transition has on this limit.


2009 ◽  
Vol 71 (3) ◽  
pp. 308-312
Author(s):  
B. I. Gizatullin ◽  
G. G. Pimenov

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