| Title:
|
Regularity and optimal control of quasicoupled and coupled heating processes (English) |
| Author:
|
Jarušek, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
81-106 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
heat equation |
| Keyword:
|
Lamé system |
| Keyword:
|
coupled system |
| Keyword:
|
viscoelasticity |
| Keyword:
|
optimal control |
| Keyword:
|
state space constraints |
| Keyword:
|
bounded stresses |
| MSC:
|
35B65 |
| MSC:
|
35M05 |
| MSC:
|
35R05 |
| MSC:
|
49J20 |
| MSC:
|
49K20 |
| MSC:
|
73U05 |
| MSC:
|
74B05 |
| MSC:
|
80A20 |
| idZBL:
|
Zbl 0854.73010 |
| idMR:
|
MR1373475 |
| DOI:
|
10.21136/AM.1996.134315 |
| . |
| Date available:
|
2009-09-22T17:50:28Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134315 |
| . |
| Reference:
|
[1] O.V. Běsov, V.P. Iljin and S.M. Nikol’skij: Integral Transformations of Functions and Imbedding Theorems.Nauka, Moskva, 1975. (Russian) |
| Reference:
|
[2] F.H. Clarke: Optimization and Nonsmooth Analysis.J. Wiley & Sons, New York, 1983. Zbl 0582.49001, MR 0709590 |
| Reference:
|
[3] I. Ekeland and R. Temam: Analyse convexe et problèmes variationnels.Dunod, Paris, 1974. MR 0463993 |
| Reference:
|
[4] J. Jarušek: Contact problems with bounded friction. Coercive case.Czech. Math. J. 33 (108) (1983), 237–261. MR 0699024 |
| Reference:
|
[5] J. Jarušek: On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes..Appl. Math. 35 (1990), 426–450. MR 1089924 |
| Reference:
|
[6] J. Jarušek: Remark to the generalized gradient method for the optimal large-scale heating problems.Probl. Control Inform. Theory 16 (1987), 89–99. MR 0907452 |
| Reference:
|
[7] P.O. Lindberg: 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. MR 0580465 |
| Reference:
|
[8] J.V. Outrata and J. Jarušek: Duality theory in mathematical programming and optimal control.Supplement to Kybernetika 20 (1984) and 21 (1985). MR 0795002 |
| Reference:
|
[9] J.L. Lions and E. Magenes: Problèmes aux limites non-homogènes et applications. Dunod, Paris.1968. |
| Reference:
|
[10] J. Nečas and I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier Sci. Publ. Co., Amsterdam-Oxford-New York, 1981. MR 0600655 |
| Reference:
|
[11] H.-J. Schmeisser and H. Triebel: Topics in Fourier Analysis and Function Spaces.Akad. Vg. Geest & Portig, Leipzig, 1987. MR 0900143 |
| Reference:
|
[12] W. Sickel: Superposition of functions in Sobolev spaces of fractional order. A survey.Partial Differential Equations, Banach Centrum Publ. vol. 27, Polish Acad. Sci., Warszawa, 1992. Zbl 0792.47062, MR 1205849 |
| Reference:
|
[13] A. Visintin: Sur le problème de Stefan avec flux non-linéaire.Boll. U.M.I. C-18 (1981), 63–86. Zbl 0478.35084, MR 0631569 |
| . |
