| Title:
|
On solvability of one special problem of coupled thermoelasticity. I. Classical boundary conditions and steady sources (English) |
| Author:
|
Horák, Jiří V. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
39-58 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35D05 |
| MSC:
|
35Q72 |
| MSC:
|
73B30 |
| MSC:
|
73C15 |
| MSC:
|
74K10 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0854.35019 |
| idMR:
|
MR1447253 |
| . |
| Date available:
|
2009-01-29T15:47:54Z |
| Last updated:
|
2012-05-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120331 |
| . |
| Reference:
|
[1] Boley B. A., Weiner J. H.: Theory of Thermal Stresses.J. Wiley and sons, New York, 1960 Zbl 1234.74001, MR 0112414 |
| Reference:
|
[2] Dafermos C. M.: On the Existence and the Asymptotic Stability of Solution to the Equations of Linear Thermoelasticity.Arch. Rational Mech. Anal., 29 (1968), 241-271. MR 0233539 |
| Reference:
|
[3] Washizu K.: Variational Methods in Elasticity and Plasticity.Pergamon Press, Oxford, 1968. Zbl 0164.26001, MR 0391679 |
| Reference:
|
[4] Kovalenko A. D.: Fundamentals of thermoelasticity.Izdatelstvo "Naukova dumka", Kiev, 1970 (in Russian). |
| Reference:
|
[5] Nowacki W.: Dynamical problems of thermoelasticity.Izdatelstvo "Mir", Moskva, 1970 (in Russian). |
| Reference:
|
[6] Aubin J. P.: Approximation of Elliptic Boundary - Value Problems.Wiley-Interscience, London, 1972. Zbl 0248.65063, MR 0478662 |
| Reference:
|
[7] Carlson D. E.: Linear Thermoelasticity.Encyklopedia of Physics, ed. S. Flüge, Volume VIa/2, Mechanics of Solids II. Springer Verlag, Berlin, 1972. |
| Reference:
|
[8] Lions J. L.: Někatoryje metody rešenija nelinejnych krajevych zadač.Izdatelstvo "Mir", Moskva, 1972 (in Russian). |
| Reference:
|
[9] Adams R. A.: Sobolev Spaces.Academic Press, New York, 1975. Zbl 0314.46030, MR 0450957 |
| Reference:
|
[10] Michlin S. G.: Variational methods in mathematical physics.Alfa, Bratislava, 1975 (in Slovak). |
| Reference:
|
[11] Truesdell C.: A first course in rational mechanics.Izdatelstvo "Mir", Moskva 1975 (in Russian). |
| Reference:
|
[12] Glowinski R., Lions J. L. , Trémolieres R.: Analyse numérique des inéquations variationnelles.Dunod, Paris, 1976. |
| Reference:
|
[13] Kufner A., John O., Fučík S.: Function Spaces.Academia, Praha, 1977. MR 0482102 |
| Reference:
|
[14] Michlin S. G.: Linějnyje uravněnija v častnych proizvodnych.Moskva, Vyššaja škola, 1977 (in Russian). |
| Reference:
|
[15] Nowacki W.: Coupled fields in mechanics of solids.In: W. T. Koiter: Theoretical and Applied Mechanics, Proceedings of the 14th IUTAM Congress, Delft, The Netherlands, 1976, North-Holland, Amsterdam, 1977. MR 0429437 |
| Reference:
|
[16] Nowinski J. L.: Theory of thermoelasticity with applications.Sijthoff & Noordhoff international Publishers, Aplhen Aan den Tijn, 1978. Zbl 0379.73004, MR 0512892 |
| Reference:
|
[17] Aubin J. P.: Applied Functional Analysis.J. Wiley and sons, New York, 1979. Zbl 0424.46001, MR 0549483 |
| Reference:
|
[18] Day W. A.: Justification of the Uncoupled and Quasistatic Approximation in a Problem of Dynamic Thermoelasticity.Arch. Rational Mech. Anal. 77 (1981), 387-396. MR 0642554 |
| Reference:
|
[19] Day W. A.: Further Justification of the Uncoupled and Quasi-Static Approximations in Thermoelasticity.Arch. Rational Mech. Anal. 79 (1982), 85-95. Zbl 0507.73003, MR 0654916 |
| Reference:
|
[20] Bock I., Lovíšek J., Štangl J.: Contact problem for two elastic beams.(in slovak), Strojnický časopis 35 (1984), No 3, 353-373 (in Slovak). |
| Reference:
|
[21] Ženíšek A.: The existence and uniqueness theorem in Biot’s consolidation theory.Aplikace matematiky, 29 (1984), No 3, 194-211. Zbl 0557.35005, MR 0747212 |
| Reference:
|
[22] Ženíšek A.: Finite element methods for coupled thermoelasticity and coupled consolidation of clay.R. A. I. R. O. Numer. Anal. 18 (1984), 183-205. MR 0743885 |
| Reference:
|
[23] Day W. A.: Heat Conduction Within Linear Thermoelasticity.Springer-Verlag, New York, 1985. Zbl 0577.73009, MR 0804043 |
| Reference:
|
[24] Horák J.: Evolution variational inequalities in thermoelasticity.MÚ ČSAV, Praha, 1985 (in Czech). |
| Reference:
|
[25] Horák J.: Solution of the problem in linear theory of coupled thermoelasticity.Ph. D. Thesis, Faculty of Natural Sciences, UP Olomouc, 1993 (in Czech). |
| Reference:
|
[26] Kačur J.: Method of Rothe in Evolution Equations.Taubner - Texte zur Mathematik, Band 80, Liepzig, 1985. MR 0834176 |
| Reference:
|
[27] Rektorys K.: Method of dicretization in time and partial differential equations.TKI, SNTL, Praha, 1985 (in Czech). |
| Reference:
|
[28] Kačur J., Ženíšek A.: Analysis of approximate solution of coupled dynamical thermoelasticity and related problems.Aplikace matematiky 31 (1986), No 3, 190-223. MR 0837733 |
| Reference:
|
[29] Tauchert T. R.: Thermal Stresses in Plates - Dynamical Problems, chapter 1.In: Richard B. Hetnarski, ed.: Thermal Stresses, vol II., North-Holland, Amsterdam, 1986. |
| . |
