Geodesic
On one problem of dynamics of thermoviscoelastic medium of Oldroid type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 68-74.

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We establish nonlocal existence theorem for the weak solution for an initial-boundary value problem for the dynamic model of thermoviscoelasticity of Oldroid type in the planar case.
Keywords: thermoviscoelastic medium, initial-boundary value problem, weak solution, fixed point.
Mots-clés : motion equations 
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V. P. Orlov; M. I. Parshin. On one problem of dynamics of thermoviscoelastic medium of Oldroid type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 68-74. http://geodesic.mathdoc.fr/item/IVM_2014_5_a7/

[1] Oldroyd J. G., Non-Newtonian flow of liquids and solids. Rheology: theory and applications, v. I, ed. F. R. Eirich, AP, New York, 1956

[2] Oskolkov A. P., “Nachalno-kraevye zadachi dlya uravnenii dvizheniya zhidkostei Kelvina–Foigta i zhidkostei Oldroida”, Tr. MIAN SSSR, 179, 1988, 126–164 | MR | Zbl

[3] Antontsev S. N., Kazhikhov A. V., Monakhov V. N., Kraevye zadachi mekhaniki, Nauka, Novosibirsk, 1983 | Zbl

[4] Agranovich Yu. Ya., Sobolevskii P. E., “Issledovanie matematicheskikh modelei vyazkouprugikh zhidkostei”, Dokl. AN USSR. Ser. A, 1989, no. 10, 3–6 | MR | Zbl

[5] Orlov V. P., “O silnykh resheniyakh nachalno-kraevoi adachi dlya regulyarizovannoi modeli nelineino-vyazkouprugoi sredy”, Matem. zametki, 84:2 (2008), 238–253 | DOI | MR | Zbl

[6] Zvyagin V. G., Orlov V. P., “Razreshimost v slabom smysle sistemy termovyazkouprugosti dlya modeli Dzheffrisa”, Izv. vuzov. Matem., 2013, no. 9, 64–69

[7] Blanchard D., Bruyère N., Guibé O., “Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation”, Commun. Pure Appl. Anal., 12:5 (2013), 2213–2227 | DOI | MR | Zbl

[8] Pawlow I., Zajaczkowski W., Global regular solutions to a Kelvin–Voigt type thermoviscoelastic system, 2011, arXiv: 1112.3176v1[math.AP] | MR

[9] Consiglieri L., “Weak solutions for a class of non-Newtonian fluids with energy transfer”, J. Math. Fluid Mech., 2:3 (2000), 267–293 | DOI | MR | Zbl

[10] Bonetti E., Bonfanti G., “Existence and uniqueness of the solution to a 3D thermoviscoelastic system”, Electronic J. Diff. Equat., 50 (2003), 1–15 | MR

[11] Krein S. G. (red.), Funktsionalnyi analiz, Nauka, M., 1972 | MR

[12] Temam R., Uravneniya Nave–Stoksa, Mir, M., 1981 | MR | Zbl

[13] Lions J.-L., Quelques methodes de resolution des problemes aux limites non lineaires, Dunod Gauthiers-Villar, Paris, 1969 | MR | Zbl

[14] Simon J., “Compact sets in the space $L^p(0,T;B)$”, Ann. Math. Pure Appl. (4), 146 (1988), 65–96 | DOI | MR

[15] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR