Abstract
This article concerns the nonlinear asymptotic analysis of the mathematical model of a multi-component poroelastic medium with the porosity balance equation. It is proved that there exist soliton-like solutions for porosity and kink-like solutions for phase velocities under conditions similar to the entropy one. It is shown that solutions appear that describe a regime of stable displacement (so-called piston displacement) and a regime similar to the Saffman–Taylor instability. It is established that the diffusion force of interaction between phases of the inner friction type causes a decrease in the amplitudes of the discontinuities. This leads to the damping of initial perturbations of stable states. Such regimes have some properties similar to those of the pendulum model in the vicinity of a stable equilibrium point.
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Radkevich, E., Wilmanski, K. On Dispersion in the Mathematical Model of Poroelastic Materials with the Balance Equation for Porosity. Journal of Mathematical Sciences 114, 1431–1449 (2003). https://doi.org/10.1023/A:1022200928241
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DOI: https://doi.org/10.1023/A:1022200928241