Approximations of singular integral equations on Lyapunov contours in Banach spaces. (English) Zbl 1089.65138
Existence theorems are proved for singular integral eguations on Lyapunov contours in Banach spaces. An approximate solution of the considered equation is constructed and the convergence to unique solution is proved and the rate of the convergence is given. These singular integral equations are widely used for the solution of a big level of problems of applied mechanics, like thermoelastoplasticy, viscoelasticity, hydrodynamics, fluid mechanics and fracture mechanics.
Reviewer: Lechoslaw Hącia (Poznań)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 45N05 | Abstract integral equations, integral equations in abstract spaces |
Keywords:
singular integral equations; Lyapunov contours in Banach spaces; Faber polynomials; Hölder’s condition; convergenceReferences:
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