| Title:
|
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes (English) |
| Author:
|
Jarušek, Jiří |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
6 |
| Year:
|
1990 |
| Pages:
|
426-450 |
| Summary lang:
|
Czech |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The continuity and boundedness of the stress to the solution of the thermoelastic system is studied first for the linear case on a strip and then for the twodimensional model involving nonlinearities, noncontinuous heating regimes and isolated boundary nonsmoothnesses of the heated body. (English) |
| Keyword:
|
nonlinear heat equation |
| Keyword:
|
Lamé system |
| Keyword:
|
noncontinuous heating regime |
| Keyword:
|
isolated boundary nonsmoothness |
| Keyword:
|
boundedness and continuity of the stresses |
| Keyword:
|
Sobolev spaces |
| Keyword:
|
Fourier transformation |
| Keyword:
|
temperature shock |
| Keyword:
|
quasi-linear thermoelasticity |
| Keyword:
|
homogeneous isotropic body |
| Keyword:
|
radiation term |
| Keyword:
|
stress field |
| MSC:
|
35K55 |
| MSC:
|
35M05 |
| MSC:
|
35R05 |
| MSC:
|
73B30 |
| MSC:
|
73U05 |
| MSC:
|
74A15 |
| MSC:
|
74B99 |
| MSC:
|
80A20 |
| idZBL:
|
Zbl 0754.73021 |
| idMR:
|
MR1089924 |
| DOI:
|
10.21136/AM.1990.104426 |
| . |
| Date available:
|
2008-05-20T18:40:11Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104426 |
| . |
| Reference:
|
[1] S. Agmon A. Douglis L. Nirenberg: Estimates near boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Part II.Comm. Pure Appl. Math. 17 (1964) 35-92. MR 0162050, 10.1002/cpa.3160170104 |
| Reference:
|
[2] O. V. Běsov V. P. lljin S. M. Nikolskij: Integral Transformations of Functions and Imbedding Theorems.(in Russian). Nauka, Moskva 1975. |
| Reference:
|
[3] P. Grisvard: Elliptic Problems in Nonsmooth Domains.Monographs and Studies in Math. 24, Pitman, Boston-London-Melbourne 1985. Zbl 0695.35060, MR 0775683 |
| Reference:
|
[4] P. Grisvard: Problemes aux limites dans les polygones, Mode d'emploi.EDF Bull. Direct. Etud. Rech. Ser. C. Math. Inform. (1986) 1, 21 - 59. Zbl 0623.35031, MR 0840970 |
| Reference:
|
[5] J. Jarušek: Contact problems with bounded friction. Coercive case.Czech. Math. J. 33 (108) (1983), 237-261. MR 0699024 |
| Reference:
|
[6] J. Jarušek: Remark to the generalized gradient method for the optimal large-scale heating problem.Probl. Control Inform. Theory 16 (1987) 2, 89-99. MR 0907452 |
| Reference:
|
[7] J. Jarušek: Optimal control of thermoelastic processes III.(in Czech). Techn. rep. Inst. Inform. Th. Autom. No. 1561, Praha 1988. |
| Reference:
|
[8] V. A. Kondratěv: Elliptic boundary value problems with conical or angular points.(in Russian). Trudy Mosk. Mat. Obšč., Vol. 16 (1967), 209-292. MR 0226187 |
| Reference:
|
[9] A. Kufner O. John S. Fučík: Function Spaces.Academia, Praha 1977. MR 0482102 |
| Reference:
|
[10] A. Kufner A. M. Sändig: Some Applications of Weighted Sobolev Spaces.Teubner-Texte Math., Band 100, Teubner V., Leipzig 1987. MR 0926688 |
| Reference:
|
[11] O. A. Ladyženskaja V. A. Solonnikov N. N. Uralceva: Linear and Quasilinear Equations of Parabolic Type.(in Russian). Nauka, Moskva 1967. MR 0241822 |
| Reference:
|
[12] J. L. Lions E. Magenes: Problèmes aux limites non-homogènes et applications.Dunod, Paris 1968. |
| Reference:
|
[13] J. Nečas: Solution of the biharmonic problem for an infinite angle.(in Czech). Časopis pěst. mat. 83 (1958), Part I, 257-286, Part. II, 399-424. |
| Reference:
|
[14] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha 1967. MR 0227584 |
| Reference:
|
[15] J. Nečas: Introduction to the Theory of Nonlinear Elliptic Equations.Teubner-Texte Math., Band 52, Teubner V., Leipzig 1983. MR 0731261 |
| Reference:
|
[16] R. H. Nochetto: Error estimates for two-phases Stefan problem in several space variables. Part II: Nonlinear flux conditions.Preprint No. 416, 1st. Anal. Numer, CNR. Pavia, Pavia 1984. MR 0775859 |
| Reference:
|
[17] A. M. Sändig U. Richter R. Sändig: The regularity of boundary value problems for the Lame equations in polygonal domain.Rostock. Math. Kolloq. 36 (1989), 21-50. MR 1006837 |
| Reference:
|
[18] A. Visintin: Sur le problème de Stefan avec flux non-lineaire.Preprint No. 230, Ist. Anal. Numer. C. N. R. Pavia, Pavia 1981. Zbl 0478.35084, MR 0631569 |
| . |
