Applications of Mathematics

, Volume 48, Issue 6, pp 469–486

On a Reliable Solution of a Volterra Integral Equation in a Hilbert Space

  • Igor Bock
  • Ján Lovíšek

DOI: 10.1023/B:APOM.0000024487.48855.d9

Cite this article as:
Bock, I. & Lovíšek, J. Applications of Mathematics (2003) 48: 469. doi:10.1023/B:APOM.0000024487.48855.d9


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.

Volterra integral equation in a Hilbert space Rothe's method maximization problem viscoelastic body 

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2003

Authors and Affiliations

  • Igor Bock
    • 1
  • Ján Lovíšek
    • 2
  1. 1.Department of Mathematics, Faculty of Electrical Engineering and Information TechnologySlovak University of TechnologyBratislavaSlovakia
  2. 2.Department of Mechanics, Faculty of Civil EngineeringSlovak University of TechnologyBratislavaSlovakia

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