| 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:
|
http://hdl.handle.net/10338.dmlcz/134693 |
| . |
| 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/j.na.2006.05.021 |
| 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 |
| . |
