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Title: Unilateral dynamic contact of von Kármán plates with singular memory (English)
Author: Bock, Igor
Author: Jarušek, Jiří
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 52
Issue: 6
Year: 2007
Pages: 515-527
Summary lang: English
Category: math
Summary: The solvability of the contact problem is proved provided the plate is simply supported. The singular memory material is assumed. This makes it possible to get a priori estimates important for the strong convergence of gradients of velocities of solutions to the penalized problem. (English)
Keyword: von Kármán plate
Keyword: unilateral dynamic contact
Keyword: singular memory
Keyword: existence of solutions
MSC: 35L85
MSC: 74D10
MSC: 74K20
idZBL: Zbl 1164.35447
idMR: MR2357578
DOI: 10.1007/s10492-007-0030-5
Date available: 2009-09-22T18:31:40Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] I. Bock, J. Jarušek: Unilateral dynamic contact of viscoelastic von Kármán plates.Adv. Math. Sci. Appl. 16 (2006), 175–187. MR 2253231
Reference: [2] I. Bock, J. Lovíšek: On unilaterally supported viscoelastic von Kármán plates with a long memory.Math. Comput. Simul. 61 (2003), 399–407. MR 1984140, 10.1016/S0378-4754(02)00095-2
Reference: [3] I. Bock, J. Lovíšek: On a contact problem for a viscoelastic von Kármán plate and its semidiscretization.Appl. Math. 50 (2005), 203–217. MR 2133727, 10.1007/s10492-005-0014-2
Reference: [4] P. G. Ciarlet, P. Rabier: Les équations de von Kármán.Springer-Verlag, Berlin, 1980. MR 0595326
Reference: [5] C. Eck, J. Jarušek, and M. Krbec: Unilateral contact problems.Variational Methods and Existence Theorems. Pure and Applied Mathematics No.  270, Chapman & Hall/CRC, Boca Raton-London-New York-Singapore, 2005. MR 2128865
Reference: [6] J. Jarušek: Solvability of unilateral hyperbolic problems involving viscoelasticity via penalization. Proc. of “Conference EQUAM”, Varenna 1992 (R.  Salvi, ed.).SAACM 3 (1993), 129–140.
Reference: [7] J. Jarušek: Solvability of the variational inequality for a drum with a memory vibrating in the presence of an obstacle.Boll. Unione Mat. Ital. VII. Ser., A 8 (1994), 113–122. MR 1273193
Reference: [8] J. Jarušek, J. V. Outrata: On sharp optimality conditions in control of contact problems with strings.Nonlinear Anal. 67 (2007), 1117–1128. MR 2325366, 10.1016/
Reference: [9] H. Koch, A. Stahel: Global existence of classical solutions to the dynamic von Kármán equations.Math. Methods Appl. Sci. 16 (1993), 581–586. MR 1233041, 10.1002/mma.1670160806
Reference: [10] J. E. Muñoz Rivera, G. Perla Menzala: Decay rates of solutions to a von Kármán system for viscoelastic plates with memory.Q.  Appl. Math. 57 (1999), 181–200. MR 1672191, 10.1090/qam/1672191
Reference: [11] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Masson/Academia, Paris/Praha, 1967. MR 0227584
Reference: [12] A. Oukit, R. Pierre: Mixed finite element for the linear plate problem: the Hermann-Miyoshi model revisited.Numer. Math. 74 (1996), 453–477. MR 1414418, 10.1007/s002110050225


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