Some integrated properties of solutions of the wave equation with non-planar boundaries

Author:
Lu Ting

Journal:
Quart. Appl. Math. **16** (1959), 373-384

MSC:
Primary 76.00

DOI:
https://doi.org/10.1090/qam/102307

MathSciNet review:
102307

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Abstract: Integrated properties of solutions of the wave equation with non-planar boundaries are found and applied to three dimensional supersonic flow problems and two dimensional diffraction problems.

**[1]**P. A. Lagerstrom and M. D. Van Dyke,*General considerations about planar and non-planar lifting systems*, Douglas Rept. No.**SM-13432**, 1949**[2]**Z. O. Bleviss,*Some integrated properties of pressure fields about supersonic wings*, J. Aero. Sci. (20)**12**, 849-851 (1953)**[3]**A. Ferri,*Recent theoretical work in supersonic aerodynamics at the Polytechnic Institute of Brooklyn*, Proceedings of the Conference on High-Speed Aeronautics, held January 20-22, 1955 at the Polytechnic Institute of Brooklyn, 1955. MR**0114467****[4]**Antonio Ferri and Joseph H. Clarke,*On the use of interfering flow fields for the reduction of drag at supersonic speeds*, J. Aero. Sci.**24**(1957), 1–18. MR**0083336****[5]**Antonio Ferri, Joseph H. Clarke, and Lu Ting,*Favorable interference in lifting systems in supersonic flow*, J. Aero. Sci.**24**(1957), 791–804. MR**0090325****[6]**O. Kellogg,*Foundations of potential theory*, Dover Publications, New York, 1953, pp. 84-88**[7]**Carlo Ferrari,*Interference between wing and body at supersonic speeds—theory and numerical application*, J. Aeronaut. Sci.**15**(1948), 317–336. MR**0025877****[8]**J. N. Nielsen,*Quasi-cylindrical theory of wing body interference at supersonic speeds and comparison with experiment*, NACA Rept. No.**1252**, 1955**[9]**Lu Ting,*Diffraction of disturbances around convex right corner with applications in acoustics and wing-body interference*, J. Aero. Sci.**24**(1957), 821–830, 844. MR**0098553****[10]**George K. Morikawa,*A non-planar boundary problem for the wave equation*, Quart. Appl. Math.**10**(1952), 129–140. MR**0047471**, https://doi.org/10.1090/S0033-569X-1952-47471-4**[11]**L. Ting,*Generalization of integral relationship with applications in wing-body interference, wing theory and diffraction of pulses*, PIBAL Rept. No.**379**, Polytechnic Institute of Brooklyn, April 1957**[12]**Lu Ting,*Diffraction and reflection of weak shocks by structures*, J. Math. Physics**32**(1953), 102–116. MR**0059725****[13]**W. R. Smith,*Diffraction of a shock wave over a rectangular notch*, Tech. Rept.**II-15**, Dept. of Physics, Princeton University, Feb. 1954**[14]**G. A. Coulter,*Two-dimensional diffraction of plane shock waves over a rectangular opening*, BRL Tech. Note No.**861**, AF SWP No.**728**, Feb. 1954

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Additional Information

DOI:
https://doi.org/10.1090/qam/102307

Article copyright:
© Copyright 1959
American Mathematical Society