Geodesic
The existence and uniqueness theorem in Biot's consolidation theory
Applications of Mathematics, Tome 29 (1984) no. 3, pp. 194-211

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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.
DOI : 10.21136/AM.1984.104085
Classification : 35A05, 35A15, 35A35, 35G05, 65N30, 73Q05
Keywords: Existence; uniqueness; variational problem; Biot’s model; compactness method; approximate solution; finite elements; Euler’s backward method 
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     author = {\v{Z}en{\'\i}\v{s}ek, Alexander},
     title = {The existence and uniqueness theorem in {Biot's} consolidation theory},
     journal = {Applications of Mathematics},
     pages = {194--211},
     publisher = {mathdoc},
     volume = {29},
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     doi = {10.21136/AM.1984.104085},
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     zbl = {0557.35005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104085/}
}
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Ženíšek, Alexander. The existence and uniqueness theorem in Biot's consolidation theory. Applications of Mathematics, Tome 29 (1984) no. 3, pp. 194-211. doi: 10.21136/AM.1984.104085

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