On the solution to a class of strongly singular linear integral equations

Author:
A. K. Gautesen

Journal:
Quart. Appl. Math. **50** (1992), 129-140

MSC:
Primary 45G05

DOI:
https://doi.org/10.1090/qam/1146628

MathSciNet review:
MR1146628

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Abstract: A strongly singular linear integral equation containing a small positive parameter is considered. This equation is transformed into a Fredholm integral equation of the second kind with a continuous kernel. The rate of convergence of the Neumann series for this integral equation is shown to be . An example from fracture mechanics is considered in detail.

**[1]**A. K. Gautesen,*On the asymptotic solution to a class of linear integral equations*, SIAM J. Appl. Math.**48**, 294-306 (1988) MR**933036****[2]**M. Hori and S. Nemat-Nasser,*Asymptotic solution to a class of strongly singular integral equations*, SIAM J. Appl. Math.**50**, 716-725 (1990) MR**1050909****[3]**S. Nemat-Nasser and M. Hori,*Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites*, Mechics of Materials**6**, 245-269 (1987)**[4]**W. E. Olmstead and A. K. Gautesen,*Asymptotic solution of some singularly perturbed Fredholm integral equations*, Z. Angew. Math. Phys.**40**, 230-244 (1989) MR**990629****[5]**J. R. Willis and S. Nemat-Nasser,*Singular perturbation solution of a class of singular integral equations*, Quart. Appl. Math.**48**, 741-753 (1990) MR**1079917**

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Additional Information

DOI:
https://doi.org/10.1090/qam/1146628

Article copyright:
© Copyright 1992
American Mathematical Society