Geodesic
Evolution of a~condensation surface in a~porous medium near the instability threshold
Informatics and Automation, Modern problems and methods in mechanics, Tome 300 (2018), pp. 86-94.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of a plane phase transition surface separating regions of soil saturated with water and with humid air; during transition to instability, the existing stable position of the phase transition surface is assumed to be sufficiently close to another phase transition surface that arises as a result of a turning point bifurcation. We show that such perturbations are described by a Kolmogorov–Petrovskii–Piskunov type equation. 
@article{TRSPY_2018_300_a5,
     author = {A. T. Il'ichev and G. G. Tsypkin},
     title = {Evolution of a~condensation surface in a~porous medium near the instability threshold},
     journal = {Informatics and Automation},
     pages = {86--94},
     publisher = {mathdoc},
     volume = {300},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_300_a5/}
}
TY  - JOUR
AU  - A. T. Il'ichev
AU  - G. G. Tsypkin
TI  - Evolution of a~condensation surface in a~porous medium near the instability threshold
JO  - Informatics and Automation
PY  - 2018
SP  - 86
EP  - 94
VL  - 300
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2018_300_a5/
LA  - ru
ID  - TRSPY_2018_300_a5
ER  - 
%0 Journal Article
%A A. T. Il'ichev
%A G. G. Tsypkin
%T Evolution of a~condensation surface in a~porous medium near the instability threshold
%J Informatics and Automation
%D 2018
%P 86-94
%V 300
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2018_300_a5/
%G ru
%F TRSPY_2018_300_a5
A. T. Il'ichev; G. G. Tsypkin. Evolution of a~condensation surface in a~porous medium near the instability threshold. Informatics and Automation, Modern problems and methods in mechanics, Tome 300 (2018), pp. 86-94. http://geodesic.mathdoc.fr/item/TRSPY_2018_300_a5/

[1] D. R. Lide, CRC handbook of chemistry and physics, 82nd ed., 2001–2002, CRC Press, Boca Raton, 2001

[2] A. T. Il'ichev, G. G. Tsypkin, “Weakly nonlinear theory for the instability of long-wave perturbations”, Dokl. Phys., 52:9 (2007), 499–501 | DOI

[3] Il'ichev A. T., Tsypkin G. G., “Catastrophic transition to instability of evaporation front in a porous medium”, Eur. J. Mech. B: Fluids, 27 (2008), 665–677 | DOI | MR

[4] A. T. Il'ichev, G. G. Tsypkin, “Instabilities of uniform filtration flows with phase transition”, J. Exp. Theor. Phys., 107 (2008), 699–711 | DOI

[5] A. Kolmogoroff, I. Petrovsky, N. Piscounoff, “Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique”, Bull. Univ. État Moscou, Math. Méc., 1:6 (1937), 1–25

[6] V. A. Shargatov, “Instability of a liquid–vapor phase transition front in inhomogeneous wettable porous media”, Fluid Dyn., 52 (2017), 146–157 | DOI | DOI | MR

[7] Shokri N., Salvucci G. D., “Evaporation from porous media in the presence of a water table”, Vadose Zone J., 10:4 (2011), 1309–1318 | DOI

[8] G. G. Tsypkin, “Stability of the evaporation and condensation surfaces in a porous medium”, Fluid Dyn., 52 (2017), 777–785 | DOI | DOI | MR

[9] Tuller M., Or D., Dudley L. M., “Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores”, Water Resour. Res., 35:7 (1999), 1949–1964 | DOI

[10] M. P. Vukalovitch, Thermodynamic Properties of Water and Steam, Mashgiz, Moscow, 1955, 1958