On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes

Jiří Jarušek

Aplikace matematiky (1990)

  • Volume: 35, Issue: 6, page 426-450
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Jarušek, Jiří. "On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes." Aplikace matematiky 35.6 (1990): 426-450. <http://eudml.org/doc/15644>.

@article{Jarušek1990,
abstract = {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.},
author = {Jarušek, Jiří},
journal = {Aplikace matematiky},
keywords = {nonlinear heat equation; Lamé system; noncontinuous heating regime; isolated boundary nonsmoothness; boundedness and continuity of the stresses; Sobolev spaces; Fourier transformation; temperature shock; quasi-linear thermoelasticity; homogeneous isotropic body; radiation term; stress field; temperature shock; quasi-linear thermoelasticity; homogeneous isotropic body; radiation term; stress field; smoothness of the boundary},
language = {eng},
number = {6},
pages = {426-450},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes},
url = {http://eudml.org/doc/15644},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Jarušek, Jiří
TI - On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 6
SP - 426
EP - 450
AB - 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.
LA - eng
KW - nonlinear heat equation; Lamé system; noncontinuous heating regime; isolated boundary nonsmoothness; boundedness and continuity of the stresses; Sobolev spaces; Fourier transformation; temperature shock; quasi-linear thermoelasticity; homogeneous isotropic body; radiation term; stress field; temperature shock; quasi-linear thermoelasticity; homogeneous isotropic body; radiation term; stress field; smoothness of the boundary
UR - http://eudml.org/doc/15644
ER -

References

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  1. S. Agmon A. Douglis L. Nirenberg, 10.1002/cpa.3160170104, Comm. Pure Appl. Math. 17 (1964) 35-92. (1964) MR0162050DOI10.1002/cpa.3160170104
  2. O. V. Běsov V. P. lljin S. M. Nikolskij, Integral Transformations of Functions and Imbedding Theorems, (in Russian). Nauka, Moskva 1975. (1975) 
  3. P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Math. 24, Pitman, Boston-London-Melbourne 1985. (1985) Zbl0695.35060MR0775683
  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. (1986) Zbl0623.35031MR0840970
  5. J. Jarušek, Contact problems with bounded friction. Coercive case, Czech. Math. J. 33 (108) (1983), 237-261. (1983) MR0699024
  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. (1987) MR0907452
  7. J. Jarušek, Optimal control of thermoelastic processes III, (in Czech). Techn. rep. Inst. Inform. Th. Autom. No. 1561, Praha 1988. (1988) 
  8. V. A. Kondratěv, Elliptic boundary value problems with conical or angular points, (in Russian). Trudy Mosk. Mat. Obšč., Vol. 16 (1967), 209-292. (1967) MR0226187
  9. A. Kufner O. John S. Fučík, Function Spaces, Academia, Praha 1977. (1977) MR0482102
  10. A. Kufner A. M. Sändig, Some Applications of Weighted Sobolev Spaces, Teubner-Texte Math., Band 100, Teubner V., Leipzig 1987. (1987) MR0926688
  11. O. A. Ladyženskaja V. A. Solonnikov N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, (in Russian). Nauka, Moskva 1967. (1967) MR0241822
  12. J. L. Lions E. Magenes, Problèmes aux limites non-homogènes et applications, Dunod, Paris 1968. (1968) 
  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. (1958) 
  14. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha 1967. (1967) MR0227584
  15. J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations, Teubner-Texte Math., Band 52, Teubner V., Leipzig 1983. (1983) MR0731261
  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. (1984) MR0775859
  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. (1989) MR1006837
  18. A. Visintin, Sur le problème de Stefan avec flux non-lineaire, Preprint No. 230, Ist. Anal. Numer. C. N. R. Pavia, Pavia 1981. (1981) Zbl0478.35084MR0631569

Citations in EuDML Documents

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  1. Jiří Jarušek, Regularity and optimal control of quasicoupled and coupled heating processes
  2. Jiří Jarušek, On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. II
  3. Jiří Jarušek, On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. III
  4. Jiří Jarušek, Dynamic contact problems with given friction for viscoelastic bodies
  5. Zdeněk Milka, Finite element solution of a stationary heat conduction equation with the radiation boundary condition

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