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optimal control; viscoelastic plate; variable thickness; pseudohyperbolic variational inequality; penalization
We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved.
[1] V. Barbu, T. Precupanu: Convexity and optimization. Sitjhoff-Noordhoff, Amsterdam, 1978.
[2] I. Bock, J. Lovíšek: Optimal control of a viscoelastic plate bending. Mathematische Nachrichten 125 (1986), 135–151. MR 0847355
[3] I. Bock, J. Lovíšek: An optimal control problem for a pseudoparabolic variational inequality. Applications of Mathematics 37 (1992), 62–80. MR 1152158
[4] H. Brézis: Problémes uniltéraux. Journal de Math. Pures et Appliqué 51 (1968), 1–168.
[5] H. Brézis: Operateurs maximaux monotones et semigroupes. North Holland, Amsterdam, 1973.
[6] J. Brilla: Linear viscoelastic plate bending analysis. Proc. XI-th Congress of Applied Mechanics, München, 1964.
[7] H. Gajewski, K. Gröger, K. Zacharias: Nichlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie, Berlin, 1974. MR 0636412
[8] J. Nečas, I. Hlaváček: Mathematical theory of elastic and elastoplastic bodies. An introduction, Elsevier, Amsterdam, 1981.
[9] O.R. Ržanicyn: Teoria polzučesti. Strojizdat, Moskva, 1968.
[10] D. Tiba: Some remarks on the control of the vibrating string with an obstacle. Revue Roumaine de Math. Pures, Appl. 29 (1984), 899–906. MR 0780134
[11] D. Tiba: Optimal control of nonsmooth distributed parameter systems. Springer-Verlag, Berlin, 1990. MR 1090951 | Zbl 0732.49002
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