Optimal design problems for a dynamic viscoelastic plate. I. Short memory material

Igor Bock

Applications of Mathematics (1995)

  • Volume: 40, Issue: 4, page 285-304
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bock, Igor. "Optimal design problems for a dynamic viscoelastic plate. I. Short memory material." Applications of Mathematics 40.4 (1995): 285-304. <http://eudml.org/doc/32920>.

@article{Bock1995,
abstract = {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.},
author = {Bock, Igor},
journal = {Applications of Mathematics},
keywords = {optimal control; viscoelastic plate; variable thickness; pseudohyperbolic variational inequality; penalization; variable thickness; optimal control; viscoelastic plate; penalization; pseudohyperbolic variational inequality},
language = {eng},
number = {4},
pages = {285-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal design problems for a dynamic viscoelastic plate. I. Short memory material},
url = {http://eudml.org/doc/32920},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Bock, Igor
TI - Optimal design problems for a dynamic viscoelastic plate. I. Short memory material
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 4
SP - 285
EP - 304
AB - 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.
LA - eng
KW - optimal control; viscoelastic plate; variable thickness; pseudohyperbolic variational inequality; penalization; variable thickness; optimal control; viscoelastic plate; penalization; pseudohyperbolic variational inequality
UR - http://eudml.org/doc/32920
ER -

References

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  2. 10.1002/mana.19861250109, Mathematische Nachrichten 125 (1986), 135–151. (1986) MR0847355DOI10.1002/mana.19861250109
  3. An optimal control problem for a pseudoparabolic variational inequality, Applications of Mathematics 37 (1992), 62–80. (1992) MR1152158
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  5. Operateurs maximaux monotones et semigroupes, North Holland, Amsterdam, 1973. (1973) 
  6. Linear viscoelastic plate bending analysis, Proc. XI-th Congress of Applied Mechanics, München, 1964. (1964) 
  7. Nichlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie, Berlin, 1974. (1974) MR0636412
  8. Mathematical theory of elastic and elastoplastic bodies, An introduction, Elsevier, Amsterdam, 1981. (1981) 
  9. Teoria polzučesti, Strojizdat, Moskva, 1968. (1968) 
  10. Some remarks on the control of the vibrating string with an obstacle, Revue Roumaine de Math. Pures, Appl. 29 (1984), 899–906. (1984) MR0780134
  11. Optimal control of nonsmooth distributed parameter systems, Springer-Verlag, Berlin, 1990. (1990) Zbl0732.49002MR1090951

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