Geodesic
Evolution of a~condensation surface in a~porous medium near the instability threshold
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 86-94

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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{TM_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 = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {86--94},
     publisher = {mathdoc},
     volume = {300},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_300_a5/}
}
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A. T. Il'ichev; G. G. Tsypkin. Evolution of a~condensation surface in a~porous medium near the instability threshold. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 86-94. http://geodesic.mathdoc.fr/item/TM_2018_300_a5/