In this paper we present a treatment of hypersingular integrals and integralequations. It is shown the equivalence of different definitions ofhypersingular integrals. Then we construct explicit analytical solution to acharacteristic equation and prove convergence of the collocation method to thissolution. Further, we expand these results to full hypersingular kernels, andgive a demonstration of the developed method to some problems of crackmechanics including crack problem for porous elastic materials, in theframework of Cowin-Nunziato model.
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