# The existence and uniqueness theorem in Biot's consolidation theory

Aplikace matematiky (1984)

- Volume: 29, Issue: 3, page 194-211
- ISSN: 0862-7940

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topŽeníšek, Alexander. "The existence and uniqueness theorem in Biot's consolidation theory." Aplikace matematiky 29.3 (1984): 194-211. <http://eudml.org/doc/15348>.

@article{Ženíšek1984,

abstract = {Existence and uniqueness theorem is established for a variational problem including Biot's model of consolidation of clay. The proof of existence is constructive and uses the compactness method. Error estimates for the approximate solution obtained by a method combining finite elements and Euler's backward method are given.},

author = {Ženíšek, Alexander},

journal = {Aplikace matematiky},

keywords = {Existence; uniqueness; variational problem; Biot’s model; compactness method; approximate solution; finite elements; Euler’s backward method; Existence; uniqueness; variational problem; Biot's model; compactness method; approximate solution; finite elements; Euler's backward method},

language = {eng},

number = {3},

pages = {194-211},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {The existence and uniqueness theorem in Biot's consolidation theory},

url = {http://eudml.org/doc/15348},

volume = {29},

year = {1984},

}

TY - JOUR

AU - Ženíšek, Alexander

TI - The existence and uniqueness theorem in Biot's consolidation theory

JO - Aplikace matematiky

PY - 1984

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 29

IS - 3

SP - 194

EP - 211

AB - Existence and uniqueness theorem is established for a variational problem including Biot's model of consolidation of clay. The proof of existence is constructive and uses the compactness method. Error estimates for the approximate solution obtained by a method combining finite elements and Euler's backward method are given.

LA - eng

KW - Existence; uniqueness; variational problem; Biot’s model; compactness method; approximate solution; finite elements; Euler’s backward method; Existence; uniqueness; variational problem; Biot's model; compactness method; approximate solution; finite elements; Euler's backward method

UR - http://eudml.org/doc/15348

ER -

## References

top- M. A. Biot, 10.1063/1.1712886, J. Appl. Phys. 12 (1941), p. 155. (1941) DOI10.1063/1.1712886
- J. R. Booker, 10.1093/qjmam/26.4.457, Quart. J. Mech. Appl. Math. 26 (1973), 457-470. (1973) DOI10.1093/qjmam/26.4.457
- J. Céa, Optimization, Dunod, Paris, 1971. (1971) Zbl0231.94026MR0298892
- A. Kufner O. John S. Fučík, Function Spaces, Academia, Prague, 1977. (1977) MR0482102
- J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, Paris, 1969. (1969) Zbl0189.40603MR0259693
- R. Теmаm, Navier-Stokes Equations, North-Holland, Amsterdam, 1977. (1977)
- M. Zlámal, 10.1137/0710022, SIAM J. Numer. Anal. 10 (1973), 229-240. (1973) MR0395263DOI10.1137/0710022
- M. Zlámal, Finite element solution of quasistationary nonlinear magnetic field, R. A.I.R.O. Anal. Num. 16 (1982), 161-191. (1982) MR0661454
- A. Ženíšek, Finite element methods for coupled thermoelasticity and coupled consolidation of clay, (To appear.) MR0743885
- K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, D. Reidel Publishing Company, Dordrecht - SNTL, Prague, 1982. (1982) Zbl0522.65059MR0689712

## Citations in EuDML Documents

top- Jiří V. Horák, On solvability of one special problem of coupled thermoelasticity. I. Classical boundary conditions and steady sources
- Alexander Ženíšek, Finite element methods for coupled thermoelasticity and coupled consolidation of clay
- Jozef Kačur, Alexander Ženíšek, Analysis of approximate solutions of coupled dynamical thermoelasticity and related problems

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