An Optimal Control Problem for A Viscoelastic Plate in a Dynamic Contact with an Obstacle

[1] BOCK, I.—JARUŠEK, J.: Unilateral dynamic contact of viscoelastic von Kármán plates, Adv. Math. Sci. Appl. 16 (2006), 175–187.Search in Google Scholar

[2] ______Dynamic contact problem for a bridge modeled by a viscoelastic von Kármán system, Z. Angew. Math. Phys. 61 (2010), 865–876.10.1007/s00033-010-0066-3Search in Google Scholar

[3] BOCK, I.—KEČKEMÉTYOVÁ, M.: An optimal design with respect to a variable thickness of a viscoelastic beam in a dynamic boundary contact, Tatra Mt. Math. Publ. 48 (2011), 15–24.Search in Google Scholar

[4] ______ Regularized optimal control problem for a beam vibrating against an elastic foundation, Tatra Mt. Math. Publ. 63 (2015), 53–71.10.1515/tmmp-2015-0020Search in Google Scholar

[5] CHRISTENSEN, R. M.: Theory of Viscoelasticity. Academic Press, New York, 1982.10.1016/B978-0-12-174252-2.50012-0Search in Google Scholar

[6] CONWAY, J. B.: A Course in Functional Analysis. Springer-Verlag, New York, 1990.Search in Google Scholar

[7] ECK C.—JARUŠEK, J.—KRBEC, M.: Unilateral Contact Problems in Mechanics. Variational Methods and Existence Theorems, in: Pure Appl. Math. (Boca Raton), Vol. 270, Boca Raton, FL, Chapman & Hall/CRC, 2005.Search in Google Scholar

[8] HASLINGER, J.—MÄKINEN, A. E.—STEBEL, J.: Shape optimization for Stokes problem with threshhold slip boundary conditions, Discrete Cont. Dyn. Syst. Ser. S. 10 (2017), 1281–1301.Search in Google Scholar

[9] JARUŠEK, J.—MÁLEK, J.—NEČAS, J.—ŠVERÁK, V.: Variational inequality for a viscous drum vibrating in the presence of an obstacle, Rend. Mat. Ser. VII. 12 (1992), 943–958.Search in Google Scholar

[10] LIONS, J. L.: Quelques Méthodes de Résolutions des Problémes aux Limites non Linéaires. Dunod, Paris, 1969.Search in Google Scholar