On a reliable solution of a Volterra integral equation in a Hilbert space

Igor Bock; Ján Lovíšek

Applications of Mathematics (2003)

  • Volume: 48, Issue: 6, page 469-486
  • ISSN: 0862-7940

Abstract

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We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to a quasistationary problem for an anisotropic viscoelastic body made of a long memory material.

How to cite

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Bock, Igor, and Lovíšek, Ján. "On a reliable solution of a Volterra integral equation in a Hilbert space." Applications of Mathematics 48.6 (2003): 469-486. <http://eudml.org/doc/33161>.

@article{Bock2003,
abstract = {We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to a quasistationary problem for an anisotropic viscoelastic body made of a long memory material.},
author = {Bock, Igor, Lovíšek, Ján},
journal = {Applications of Mathematics},
keywords = {Volterra integral equation in a Hilbert space; Rothe’s method; maximization problem; viscoelastic body; Volterra integral equation in a Hilbert space; Rothe's method; maximization problem; viscoelastic body},
language = {eng},
number = {6},
pages = {469-486},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a reliable solution of a Volterra integral equation in a Hilbert space},
url = {http://eudml.org/doc/33161},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Bock, Igor
AU - Lovíšek, Ján
TI - On a reliable solution of a Volterra integral equation in a Hilbert space
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 6
SP - 469
EP - 486
AB - We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to a quasistationary problem for an anisotropic viscoelastic body made of a long memory material.
LA - eng
KW - Volterra integral equation in a Hilbert space; Rothe’s method; maximization problem; viscoelastic body; Volterra integral equation in a Hilbert space; Rothe's method; maximization problem; viscoelastic body
UR - http://eudml.org/doc/33161
ER -

References

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