On a 3D-Hypersingular Equation of a Problem for a Crack

Samko, Stefan

Fractional Calculus and Applied Analysis (2011)

  • Volume: 14, Issue: 1, page 19-30
  • ISSN: 1311-0454

Abstract

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MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.

How to cite

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Samko, Stefan. "On a 3D-Hypersingular Equation of a Problem for a Crack." Fractional Calculus and Applied Analysis 14.1 (2011): 19-30. <http://eudml.org/doc/219572>.

@article{Samko2011,
abstract = {MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.},
author = {Samko, Stefan},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Fractional Operator; Hypersingular Integrals; Diffraction; Cracks; Potential Kernel; Singular Operator; fractional operator; hypersingular integrals; diffraction},
language = {eng},
number = {1},
pages = {19-30},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On a 3D-Hypersingular Equation of a Problem for a Crack},
url = {http://eudml.org/doc/219572},
volume = {14},
year = {2011},
}

TY - JOUR
AU - Samko, Stefan
TI - On a 3D-Hypersingular Equation of a Problem for a Crack
JO - Fractional Calculus and Applied Analysis
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 14
IS - 1
SP - 19
EP - 30
AB - MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.
LA - eng
KW - Fractional Operator; Hypersingular Integrals; Diffraction; Cracks; Potential Kernel; Singular Operator; fractional operator; hypersingular integrals; diffraction
UR - http://eudml.org/doc/219572
ER -

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