Unilateral dynamic contact of von Kármán plates with singular memory

Igor Bock; Jiří Jarušek

Applications of Mathematics (2007)

  • Volume: 52, Issue: 6, page 515-527
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Bock, Igor, and Jarušek, Jiří. "Unilateral dynamic contact of von Kármán plates with singular memory." Applications of Mathematics 52.6 (2007): 515-527. <http://eudml.org/doc/33306>.

@article{Bock2007,
abstract = {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.},
author = {Bock, Igor, Jarušek, Jiří},
journal = {Applications of Mathematics},
keywords = {von Kármán plate; unilateral dynamic contact; singular memory; existence of solutions; von Kármán plate; unilateral dynamic contact; singular memory; existence of solutions},
language = {eng},
number = {6},
pages = {515-527},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unilateral dynamic contact of von Kármán plates with singular memory},
url = {http://eudml.org/doc/33306},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Bock, Igor
AU - Jarušek, Jiří
TI - Unilateral dynamic contact of von Kármán plates with singular memory
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 6
SP - 515
EP - 527
AB - 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.
LA - eng
KW - von Kármán plate; unilateral dynamic contact; singular memory; existence of solutions; von Kármán plate; unilateral dynamic contact; singular memory; existence of solutions
UR - http://eudml.org/doc/33306
ER -

References

top
  1. Unilateral dynamic contact of viscoelastic von Kármán plates, Adv. Math. Sci. Appl. 16 (2006), 175–187. (2006) MR2253231
  2. 10.1016/S0378-4754(02)00095-2, Math. Comput. Simul. 61 (2003), 399–407. (2003) MR1984140DOI10.1016/S0378-4754(02)00095-2
  3. 10.1007/s10492-005-0014-2, Appl. Math. 50 (2005), 203–217. (2005) MR2133727DOI10.1007/s10492-005-0014-2
  4. Les équations de von Kármán, Springer-Verlag, Berlin, 1980. (1980) MR0595326
  5. Unilateral contact problems, Variational Methods and Existence Theorems. Pure and Applied Mathematics No.  270, Chapman & Hall/CRC, Boca Raton-London-New York-Singapore, 2005. (2005) MR2128865
  6. Solvability of unilateral hyperbolic problems involving viscoelasticity via penalization. Proc. of “Conference EQUAM”, Varenna 1992 (R.  Salvi, ed.), SAACM 3 (1993), 129–140. (1993) 
  7. 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. (1994) MR1273193
  8. 10.1016/j.na.2006.05.021, Nonlinear Anal. 67 (2007), 1117–1128. (2007) MR2325366DOI10.1016/j.na.2006.05.021
  9. 10.1002/mma.1670160806, Math. Methods Appl. Sci. 16 (1993), 581–586. (1993) MR1233041DOI10.1002/mma.1670160806
  10. 10.1090/qam/1672191, Q.  Appl. Math. 57 (1999), 181–200. (1999) MR1672191DOI10.1090/qam/1672191
  11. Les méthodes directes en théorie des équations elliptiques, Masson/Academia, Paris/Praha, 1967. (1967) MR0227584
  12. 10.1007/s002110050225, Numer. Math. 74 (1996), 453–477. (1996) MR1414418DOI10.1007/s002110050225

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.