×

On a viscoelastoplastic porous medium problem with nonlinear interaction. (English) Zbl 1458.74039

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
76S05 Flows in porous media; filtration; seepage
35Q74 PDEs in connection with mechanics of deformable solids
35Q35 PDEs in connection with fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] H. Al Baba, N. Chemetov, Š. Nečasová, and B. Muha, Strong solutions in \(L^2\) framework for fluid-rigid body interaction problem: Mixed case, Topol. Methods Nonlinear Anal., 52 (2018), pp. 337-350. · Zbl 1410.35108
[2] B. Albers, Modeling the hysteretic behavior of the capillary pressure in partially saturated porous media-a review, Acta Mech., 225 (2014), pp. 2163-2189. · Zbl 1302.74129
[3] B. Albers and P. Krejčí, Unsaturated porous media flow with thermomechanical interaction, Math. Methods Appl. Sci., 39 (2016), pp. 2220-2238. · Zbl 1338.76116
[4] F. Bagagiolo and A. Visintin, Hysteresis in filtration through porous media, Z. Anal. Anwend., 19 (2000), pp. 977-997. · Zbl 0977.35072
[5] F. Bagagiolo and A. Visintin, Porous media filtration with hysteresis, Adv. Math. Sci. Appl., 14 (2004), pp. 379-403. · Zbl 1073.76066
[6] O. V. Besov, V. P. Il’in, and S. M. Nikol’skii, Integral Representations of Functions and Imbedding Theorems: Vols. I & II, Scripta Ser. Math., V. H. Winston & Sons, Washington, D.C.; Halsted Press [John Wiley & Sons], New York-Toronto, Ont.-London, 1978, 1979.
[7] M. A. Biot, General theory of three-dimensional consolidation, J. Appl. Phys., 12 (1941), pp. 155-164. · JFM 67.0837.01
[8] B. Detmann, P. Krejčí, and E. Rocca, Solvability of an unsaturated porous media flow problem with thermomechanical interaction, SIAM J. Math. Anal., 48 (2016), pp. 4175-4201, https://doi.org/10.1137/16M1056365. · Zbl 1364.76218
[9] E. Feireisl, D. Hilhorst, H. Petzeltová, and P. Takáč, Mathematical analysis of variable density flows in porous media, J. Evol. Equ., 16 (2016), pp. 1-19. · Zbl 1376.35090
[10] E. Feireisl, J. MikyŠka, H. Petzeltová, and P. Takáč, On the motion of chemically reacting fluids through porous medium, in From Particle Systems to Partial Differential Equations (PSPDE 2015), Springer Proc. Math. Statist. 209, P. Gonçalves and A. Soares, eds., Springer, Cham, 2017, pp. 139-152. · Zbl 1391.76720
[11] D. Flynn, H. McNamara, J. P. O’Kane, and A. V. Pokrovskii, Application of the Preisach model to soil-moisture hysteresis, in The Science of Hysteresis, Vol. 3, G. Bertotti and I. Mayergoyz, eds., Academic Press, Oxford, 2006, pp. 689-744. · Zbl 1136.76048
[12] S. Fučík and A. Kufner, Nonlinear Differential Equations, Stud. Appl. Mech. 2, Elsevier Scientific Publ. Co., Amsterdam, New York, 1980. · Zbl 0426.35001
[13] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983. · Zbl 0562.35001
[14] R. Haverkamp, P. Reggiani, P. J. Ross, and J.-Y. Parlange, Soil water hysteresis prediction model based on theory and geometric scaling, in Environmental Mechanics, Water, Mass and Energy Transfer in the Biosphere, P. A. C. Raats, D. Smiles, and A.W. Warrick, eds., American Geophysical Union, Washington, D.C., 2002, pp. 213-246.
[15] A. Hundertmark-ZauŠková, M. Lukáčová-Medvi\vdová, and Š. Nečasová, On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid, J. Math. Soc. Japan, 68 (2016), pp. 193-243. · Zbl 1334.76032
[16] P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, GAKUTO Internat. Ser. Math. Sci. Appl. 8, Gakkōtosho Co., Ltd., Tokyo, 1996. · Zbl 1187.35003
[17] P. Krejčí, Boundedness of solutions to a degenerate diffusion equation, in Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs, P. Colli, A. Favini, E. Rocca, G. Schimperna, and J. Sprekels, eds., Springer INdAM Ser. 22, Springer, Cham, 2017, pp. 305-326. · Zbl 1387.35379
[18] P. Krejčí and L. Panizzi, Regularity and uniqueness in quasilinear parabolic systems, Appl. Math., 56 (2011), pp. 341-370. · Zbl 1240.35234
[19] P. Krejčí, E. Rocca, and J. Sprekels, Unsaturated deformable porous media flow with thermal phase transition, Math. Models Methods Appl. Sci., 27 (2017), pp. 2675-2710. · Zbl 1386.76163
[20] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type, Izdat. “Nauka”, Moscow, 1967 (in Russian).
[21] O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Equations of Elliptic Type, 2nd ed. rev., Izdat. “Nauka”, Moscow, 1973 (in Russian).
[22] P. D. Lax and A. N. Milgram, Parabolic equations: Contributions to the theory of partial differential equations, Ann. Math. Stud., 33 (1954), pp. 167-190. · Zbl 0058.08703
[23] J. Lemaitre and J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, Cambridge, 1990.
[24] J. Nečas and I. Hlaváček, Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Stud. Appl. Mech. 3, Elsevier Scientific Publishing Co., Amsterdam-New York, 1980. · Zbl 0448.73009
[25] M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, 2nd ed., Texts Appl. Math. 13, Springer-Verlag, New York, 2004. · Zbl 1072.35001
[26] R. E. Showalter, Diffusion in deforming porous media, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10 (2003), pp. 661-678. · Zbl 1122.76394
[27] R. E. Showalter and U. Stefanelli, Diffusion in poro-plastic media, Math. Methods Appl. Sci., 27 (2004), pp. 2131-2151. · Zbl 1095.74011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.