Asymptotic stability of solutions to the porous media system with hysteresis

0531877 - MÚ 2021 RIV US eng J - Journal Article
Eleuteri, M. - Krejčí, Pavel
Asymptotic stability of solutions to the porous media system with hysteresis.
SIAM Journal on Mathematical Analysis. Roč. 52, č. 4 (2020), s. 3962-3989. ISSN 0036-1410. E-ISSN 1095-7154
Institutional support: RVO:67985840
Keywords : porous media system * hysteresis * asymptotic behavior
OECD category: Pure mathematics
Impact factor: 1.860, year: 2020
Method of publishing: Limited access
https://doi.org/10.1137/19M1271415

The long time behavior of solutions to the autonomous PDE system describing fluid diffusion in a viscoelastic porous medium with capillary hysteresis is studied with homogeneous Dirichlet conditions for the displacement of the solid and homogeneous Neumann boundary conditions for the capillary pressure. Although the set of possible equilibria is very large, a detailed investigation of the hysteresis memory dynamics shows that all global solution trajectories converge to an equilibrium in the state space of all admissible memory configurations as time tends to infinity.
Permanent Link: http://hdl.handle.net/11104/0310515