An expression for Green’s function for a particular Tricomi problem
Author:
Paul Germain
Journal:
Quart. Appl. Math. 14 (1956), 113-124
MSC:
Primary 35.0X
DOI:
https://doi.org/10.1090/qam/79713
MathSciNet review:
79713
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F. Tricomi, Sulle equazioni lineari alle derivate parziali di $2^{o}$ ordine di tipo misto, Reale Accad. Lincei, Mem. Classe Sc. Fisiche Math. Nat. (5) 14, 133-247 (1923).
- P. Germain and R. Bader, Sur quelques problèmes relatifs à l’équation de type mixte de Tricomi, O.N.E.R.A. Publ. 1952 (1952), no. 54, ii+57 (French). MR 52665
- Paul Germain and Roger Bader, Sur le problème de Tricomi, Rend. Circ. Mat. Palermo (2) 2 (1953), 53–70 (French). MR 61746, DOI https://doi.org/10.1007/BF02871677
- Paul Germain and Marc Liger, Une nouvelle approximation pour l’étude des écoulements subsoniques et transsoniques, C. R. Acad. Sci. Paris 234 (1952), 1846–1848 (French). MR 54439
M. Liger, Nouvelles équations approchées pour l’étude des écoulements subsoniques et transsoniques, Publ. ONERA No. 64 (1953).
- P. Germain, New applications of Tricomi solutions to transonic flow, Proceedings of the Second U. S. National Congress of Applied Mechanics, Ann Arbor, 1954, American Society of mechanical Engineers, New York, 1955, pp. 659–666. MR 0079465
- P. Germain and R. Bader, Solutions élémentaires de certaines équations aux dérivées partielles du type mixte, Bull. Soc. Math. France 81 (1953), 145–174 (French). MR 58834
- P. Germain, Remarks on the theory of partial differential equations of mixed type and applications to the study of transonic flow, Comm. Pure Appl. Math. 7 (1954), 117–143. MR 65792, DOI https://doi.org/10.1002/cpa.3160070109
- Laurent Schwartz, Théorie des distributions. Tome II, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1122, Hermann & Cie., Paris, 1951 (French). Publ. Inst. Math. Univ. Strasbourg 10. MR 0041345
- Rudolph E. Langer, The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to a turning point, Trans. Amer. Math. Soc. 67 (1949), 461–490. MR 33420, DOI https://doi.org/10.1090/S0002-9947-1949-0033420-2
- Alexander Weinstein, Discontinuous integrals and generalized potential theory, Trans. Amer. Math. Soc. 63 (1948), 342–354. MR 25023, DOI https://doi.org/10.1090/S0002-9947-1948-0025023-X
- Julian Cole, Drag of a finite wedge at high subsonic speeds, J. Math. Physics 30 (1951), 79–92. MR 0057688
P. Germain, Remarks on transforms and boundary value problems (unpublished).
A. Erdelyi, Higher transcendental functions, Bateman Manuscript Project, Volume I.
- F. Frankl, On the problems of Chaplygin for mixed sub- and supersonic flows, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 9 (1945), 121–143 (Russian, with English summary). MR 0015981
E. Picard, Leçons sur quelques types simples d’équations aux dérivées partielles, Gauthier-Villars, Paris (1927).
E. Goursat, Cours d’analyse mathématique, vol. 3, Gauthier-Villars, Paris (1942).
F. Tricomi, Sulle equazioni lineari alle derivate parziali di $2^{o}$ ordine di tipo misto, Reale Accad. Lincei, Mem. Classe Sc. Fisiche Math. Nat. (5) 14, 133-247 (1923).
P. Germain and R. Bader, Sur quelques problèmes relatifs À l’équation de type mixte de Tricomi, Pub. ONERA, No. 54 (1952).
P. Germain and R. Bader, Sur le problème de Tricomi, Rend. Circ. Palermo (II) 2, 1 (1953).
P. Germain and M. Liger, Une nouvelle approximation pour l’étude des écoulements subsoniques et transsoniques, C. R. Ac. Sc. 234, 1846-1848 (1952).
M. Liger, Nouvelles équations approchées pour l’étude des écoulements subsoniques et transsoniques, Publ. ONERA No. 64 (1953).
P. Germain, New applications of Tricomi solutions to transonic flow, Second National Congress of Applied Mechanics, 1954.
P. Germain and R. Bader, Solutions élémentaires de certaines équations aux dérivées partielles du type mixte, Bull. Soc. Math. France, 1953.
P. Germain, Remarks on the theory of partial differential equations of mixed type and applications to the study of transonic flow, Communications of Pure and Applied Math. 1954.
L. Schwartz, Théorie des distributions, Hermann Paris, 1951.
R. E. Langer, The asymptotic solutions of ordinary linear differential equations of the second order with special reference to a turning point, Trans. Am. Math. Soc. 67, 461-490 (1949).
A. Weinstein, Discontinuous integrals and generalized potential theory, Transactions Amer. Math. Soc. 63, 342-354 (1948).
J. D. Cole, Drag of finite wedge at high subsonic speeds, Journ. Math. Phys. 30, 79-93 (1951).
P. Germain, Remarks on transforms and boundary value problems (unpublished).
A. Erdelyi, Higher transcendental functions, Bateman Manuscript Project, Volume I.
F. Frankl, On the problem of Chaplygin for mixed sub- and supersonic flows, Bulletin Acad. Sci. U.R.S.S., Serie Math. 9, 121-143 (1945).
E. Picard, Leçons sur quelques types simples d’équations aux dérivées partielles, Gauthier-Villars, Paris (1927).
E. Goursat, Cours d’analyse mathématique, vol. 3, Gauthier-Villars, Paris (1942).
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Article copyright:
© Copyright 1956
American Mathematical Society
