Regularity and optimal control of quasicoupled and coupled heating processes

Jiří Jarušek

Applications of Mathematics (1996)

  • Volume: 41, Issue: 2, page 81-106
  • ISSN: 0862-7940

Abstract

top
Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions of such systems, the technique of spaces of Běsov-Sobolev type is essentially employed and the possibility of its use when solving optimization problems is studied.

How to cite

top

Jarušek, Jiří. "Regularity and optimal control of quasicoupled and coupled heating processes." Applications of Mathematics 41.2 (1996): 81-106. <http://eudml.org/doc/32939>.

@article{Jarušek1996,
abstract = {Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions of such systems, the technique of spaces of Běsov-Sobolev type is essentially employed and the possibility of its use when solving optimization problems is studied.},
author = {Jarušek, Jiří},
journal = {Applications of Mathematics},
keywords = {heat equation; Lamé system; coupled system; viscoelasticity; optimal control; state space constraints; bounded stresses; Lamé system; continuity; boundedness; viscoelasticity; optimization; spaces of Besov-Sobolev type},
language = {eng},
number = {2},
pages = {81-106},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regularity and optimal control of quasicoupled and coupled heating processes},
url = {http://eudml.org/doc/32939},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Jarušek, Jiří
TI - Regularity and optimal control of quasicoupled and coupled heating processes
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 2
SP - 81
EP - 106
AB - Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions of such systems, the technique of spaces of Běsov-Sobolev type is essentially employed and the possibility of its use when solving optimization problems is studied.
LA - eng
KW - heat equation; Lamé system; coupled system; viscoelasticity; optimal control; state space constraints; bounded stresses; Lamé system; continuity; boundedness; viscoelasticity; optimization; spaces of Besov-Sobolev type
UR - http://eudml.org/doc/32939
ER -

References

top
  1. Integral Transformations of Functions and Imbedding Theorems, Nauka, Moskva, 1975. (Russian) (1975) 
  2. Optimization and Nonsmooth Analysis, J. Wiley & Sons, New York, 1983. (1983) Zbl0582.49001MR0709590
  3. Analyse convexe et problèmes variationnels, Dunod, Paris, 1974. (1974) MR0463993
  4. Contact problems with bounded friction. Coercive case, Czech. Math. J. 33 (108) (1983), 237–261. (1983) MR0699024
  5. On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes., Appl. Math. 35 (1990), 426–450. (1990) MR1089924
  6. Remark to the generalized gradient method for the optimal large-scale heating problems, Probl. Control Inform. Theory 16 (1987), 89–99. (1987) MR0907452
  7. A generalization of Fenchel conjugation giving generalized Lagrangians and symmetric nonconvex duality, Survey of Math. programming (Proc. 9th Internat. Math. Program. Symp.), A. Prékopa (ed.), Budapest, 1976, pp. 249–267. (1976) MR0580465
  8. Duality theory in mathematical programming and optimal control, Supplement to Kybernetika 20 (1984) and 21 (1985). (1984) and 21 (1985) MR0795002
  9. Problèmes aux limites non-homogènes et applications. Dunod, Paris, 1968. (1968) 
  10. Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier Sci. Publ. Co., Amsterdam-Oxford-New York, 1981. (1981) MR0600655
  11. Topics in Fourier Analysis and Function Spaces, Akad. Vg. Geest & Portig, Leipzig, 1987. (1987) MR0900143
  12. Superposition of functions in Sobolev spaces of fractional order. A survey, Partial Differential Equations, Banach Centrum Publ. vol. 27, Polish Acad. Sci., Warszawa, 1992. (1992) Zbl0792.47062MR1205849
  13. Sur le problème de Stefan avec flux non-linéaire, Boll. U.M.I. C-18 (1981), 63–86. (1981) Zbl0478.35084MR0631569

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.