Attractors in models of porous media flow

Akhmetzyanov, A. V.; Kushner, Alexei G.; Lychagin, Valentin

doi:10.1134/s1064562417010239

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Finite Dimensional Dynamics1

Case B1

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Cited by 10 publications

(2 citation statements)

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“…Definition 3 [10] Dynamics ( 4) is said to be an attractor for the solution u(t, x) of evolutionary equation (6) if…”

Section: Finite Dimensional Dynamicsmentioning

confidence: 99%

See 1 more Smart Citation

Critical phenomena and singular solutions in non-stationary filtration of real gases

Lychagin,

Roop

2020

Preprint

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In this paper, we study non-stationary filtration of real gases in porous media. Thermodynamic state of the medium is given by van der Waals state equations. Solutions for non-stationary filtration equation are obtained by means of finite dimensional dynamics. The analysis of phase transitions along the flow in case of isentropic and isenthalpic processes is presented as well as singular properties of solutions obtained are discussed. Domains in the jet space where the dynamics found is an attractor are shown.

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“…Definition 3 [10] Dynamics ( 4) is said to be an attractor for the solution u(t, x) of evolutionary equation (6) if…”

Section: Finite Dimensional Dynamicsmentioning

confidence: 99%

“…Solution ( 24) is a travelling wave, which coincides with (15) by choosing constants C1 and C2. Inequalities (25) for given c1 and c2 define domains in the jet space J 2 (π) where dynamics ( 19) is an attractor for equation (10). Sections of these domains for various values y2 are shown in figure 7.…”

Section: Case Bmentioning

confidence: 99%