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

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

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Authors and Affiliations 1. Department of Mathematics, Faculty of Electrical Engineering and Information Technology Slovak University of Technology Bratislava Slovakia 2. Department of Mechanics, Faculty of Civil Engineering Slovak University of Technology Bratislava Slovakia