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On a Reliable Solution of a Volterra Integral Equation in a Hilbert Space
Authors:Igor Bock  Ján Loví?ek
Institution:(1) Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, 812 19 Bratislava, Slovakia;(2) Department of Mechanics, Faculty of Civil Engineering, Slovak University of Technology, 813 68 Bratislava, Slovakia
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.
Keywords:Volterra integral equation in a Hilbert space  Rothe's method  maximization problem  viscoelastic body
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