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Regularity and optimal control of quasicoupled and coupled heating processes. (English) Zbl 0854.73010

Summary: Sufficient conditions for continuity and boundedness of stresses in three-dimensional linearized coupled thermoelastic systems including viscoelasticity are derived, and the optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is investigated. Due to the heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions for such systems, the technique of spaces of Besov-Sobolev type is employed, and the possibility of its use in optimization problems is studied.

MSC:

74B05 Classical linear elasticity
80A20 Heat and mass transfer, heat flow (MSC2010)
49J20 Existence theories for optimal control problems involving partial differential equations
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References:

[1] O.V. Běsov, V.P. Iljin and S.M. Nikol’skij: Integral Transformations of Functions and Imbedding Theorems. Nauka, Moskva, 1975.
[2] F.H. Clarke: Optimization and Nonsmooth Analysis. J. Wiley & Sons, New York, 1983. · Zbl 0582.49001
[3] I. Ekeland and R. Temam: Analyse convexe et problèmes variationnels. Dunod, Paris, 1974. · Zbl 0281.49001
[4] J. Jarušek: Contact problems with bounded friction. Coercive case. Czech. Math. J. 33 (108) (1983), 237-261. · Zbl 0519.73095
[5] J. Jarušek: On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. Appl. Math. 35 (1990), 426-450. · Zbl 0754.73021
[6] J. Jarušek: Remark to the generalized gradient method for the optimal large-scale heating problems. Probl. Control Inform. Theory 16 (1987), 89-99. · Zbl 0647.73047
[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.
[8] J.V. Outrata and J. Jarušek: Duality theory in mathematical programming and optimal control. Supplement to Kybernetika 20 (1984) and 21 (1985).
[9] J.L. Lions and E. Magenes: Problèmes aux limites non-homogènes et applications. Dunod, Paris. 1968.
[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.
[11] H.-J. Schmeisser and H. Triebel: Topics in Fourier Analysis and Function Spaces. Akad. Vg. Geest & Portig, Leipzig, 1987. · Zbl 0661.46024
[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
[13] A. Visintin: Sur le problème de Stefan avec flux non-linéaire. Boll. U.M.I. C-18 (1981), 63-86. · Zbl 0478.35084
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