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On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Gil, Alexey, Samko, Stefan (2010)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.We give a procedure to reduce a hypersingular integral equation, arising in 2d diffraction problems on cracks in elastic media, to a Fredholm integral equation of the second kind, to which it is easier and more effectively to apply numerical methods than to the initial hypersingular equation.

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

Igor Bock, Ján Lovíšek (2003)

Applications of Mathematics

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...

On stability and robust stability of positive linear Volterra equations in Banach lattices

Satoru Murakami, Pham Ngoc (2010)

Open Mathematics

We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.

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