END-POINT BEHAVIOR OF SOLUTIONS TO HYPERSINGULAR INTEGRAL-EQUATIONS

被引：49
作者：
MARTIN, PA
机构：
来源：
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1991年 / 432卷 / 1885期
关键词：
D O I：
10.1098/rspa.1991.0019
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We consider one-dimensional hypersingular integral equations over finite intervals; the integral must be interpreted as a finite-part integral. Such equations arise naturally in various physical situations, involving thin rigid bodies or cracks; examples are given. A method is developed for determining the behaviour of the solution to a hypersingular integral equation near the end-points of the interval of integration. The method uses the Mellin transform. Several examples are worked out in detail.
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页码：301 / 320
页数：20
相关论文
共 31 条
[1]  
Barenblatt GI., 1962, ADV APPL MECH, V7, P55, DOI DOI 10.1016/S0065-2156(08
[2]  
Bleistein N., 1975, ASYMPTOTIC EXPANSION
[3]  
Bueckner H. F., 1973, Mechanics of fracture. Vol.1: Methods of analysis and solutions of crack problems, P239
[4]  
COSTABEL M, 1983, J INTEGRAL EQUAT, V5, P353
[5]   THE NORMAL DERIVATIVE OF THE DOUBLE-LAYER POTENTIAL ON POLYGONS AND GALERKIN APPROXIMATION [J].
COSTABEL, M ;
STEPHAN, E .
APPLICABLE ANALYSIS, 1983, 16 (03) :205-228
[6]  
CUMINATO JA, 1990, MATH ENG IND, V2, P233
[7]  
Davies B., 1985, INTEGRAL TRANSFORMS
[8]  
Duduchava R., 1982, INTEGRAL EQUATIONS O, V5, P475
[9]  
ERDOGAN F, 1973, MECHANICS FRACTURE, V1, P386
[10]   DIFFRACTION OF WATER WAVES BY A SUBMERGED VERTICAL PLATE [J].
EVANS, DV .
JOURNAL OF FLUID MECHANICS, 1970, 40 :433-&
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