Application of the kernel function for the computation of flows of compressible fluids
Author:
Stefan Bergman
Journal:
Quart. Appl. Math. 26 (1968), 301-310
MSC:
Primary 76.35; Secondary 30.00
DOI:
https://doi.org/10.1090/qam/253628
MathSciNet review:
253628
Full-text PDF Free Access
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Additional Information
S. Bergman, Zur Theorie der Funktionen, die eine lineare partielle Differentialgleichung befriedigen, Mat. Sb. (Recueil Math.) [2] 44, 1169–1198 (1937)
S. Bergman, The hodograph method in the theory of compressible fluids, Suppl. to Fluid Dynamics (R. von Mises and K. O. Friedrichs, eds.), Brown University Graduate School, Providence, R. I., 1942, pp. 1–40
- Stefan Bergman, A formula for the stream function of certain flows, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 276–281. MR 10079, DOI https://doi.org/10.1073/pnas.29.9.276
- Stefan Bergman, On two-dimensional flows of compressible fluids, Tech. Notes Nat. Adv. Comm. Aeronaut. 1945 (1945), no. 972, 81 pp. (3 plates). MR 0014874
- Stefan Bergman, Two-dimensional subsonic flows of a compressible fluid and their singularities, Trans. Amer. Math. Soc. 62 (1947), 452–498. MR 26498, DOI https://doi.org/10.1090/S0002-9947-1947-0026498-1
- Stefan Bergman, Integral operators in the theory of linear partial differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 23, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0141880
- Stefan Bergman, On representation of stream functions of subsonic and supersonic flows of compressible fluids, J. Rational Mech. Anal. 4 (1955), 883–905. MR 74206, DOI https://doi.org/10.1512/iumj.1955.4.54033
- Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR 0038439
- Stefan Bergman and John G. Herriot, Numerical solution of boundary-value problems by the method of integral operators, Numer. Math. 7 (1965), 42–65. MR 176619, DOI https://doi.org/10.1007/BF01397972
- S. Bergman and M. Schiffer, Kernel functions in the theory of partial differential equations of elliptic type, Duke Math. J. 15 (1948), 535–566. MR 25662
- Stefan Bergman and M. Schiffer, Kernel functions and elliptic differential equations in mathematical physics, Academic Press Inc., New York, N. Y., 1953. MR 0054140
- Lipman Bers, On a method of constructing two-dimensional subsonic compressible flows around closed profiles, Tech. Notes Nat. Adv. Comm. Aeronaut. 1945 (1945), no. 969, 61 pp. (4 plates). MR 0015989
- Lipman Bers, An existence theorem in two-dimensional gas dynamics, Proc. Symposia Appl. Math., Vol. I, American Mathematical Society, New York, N. Y., 1949, pp. 41–46. MR 0030382
- Lipman Bers, Mathematical aspects of subsonic and transonic gas dynamics, Surveys in Applied Mathematics, Vol. 3, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096477
- Robert Finn, Isolated singularities of solutions of non-linear partial differential equations, Trans. Amer. Math. Soc. 75 (1953), 385–404. MR 58826, DOI https://doi.org/10.1090/S0002-9947-1953-0058826-8
L. A. Fine, Some qualitative results of a plane subsonic flow, Dissertation, Stanford University, 1965
- R. Finn and D. Gilbarg, Asymptotic behavior and uniquenes of plane subsonic flows, Comm. Pure Appl. Math. 10 (1957), 23–63. MR 86556, DOI https://doi.org/10.1002/cpa.3160100102
- David Gilbarg, Comparison methods in the theory of subsonic flows, J. Rational Mech. Anal. 2 (1953), 233–251. MR 54435, DOI https://doi.org/10.1512/iumj.1953.2.52011
- Fritz John, General properties of solutions of linear elliptic partial differential equations, Proceedings of the Symposium on Spectral Theory and Differential Problems, Oklahoma Agricultural and Mechanical College, Stillwater, Okla., 1951, pp. 113–175. MR 0043990
- G. S. S. Ludford, The behavior at infinity of the potential function of a two dimensional subsonic compressible flow, J. Math. Physics 30 (1951), 117–130. MR 0044303
- Richard von Mises, Mathematical theory of compressible fluid flow, Academic Press, Inc., New York, N.Y., 1958. Applied mathematics and mechanics. Vol. 3. MR 0094996
- Menahem Schiffer, Various types of orthogonalization, Duke Math. J. 17 (1950), 329–366. MR 39071
- J. M. Stark, Application of Bergman’s integral operators to transonic flows, Internat. J. Non-Linear Mech. 1 (1966), 17–34 (English, with French, German and Russian summaries). MR 230508, DOI https://doi.org/10.1016/0020-7462%2866%2990015-1
S. Bergman, Zur Theorie der Funktionen, die eine lineare partielle Differentialgleichung befriedigen, Mat. Sb. (Recueil Math.) [2] 44, 1169–1198 (1937)
S. Bergman, The hodograph method in the theory of compressible fluids, Suppl. to Fluid Dynamics (R. von Mises and K. O. Friedrichs, eds.), Brown University Graduate School, Providence, R. I., 1942, pp. 1–40
S. Bergman, A formula for the stream function of certain flows, Proc. Nat. Acad. Sci. U. S. 29, 276–281 (1943)
S. Bergman, On two-dimensional flows of compressible fluids, NACA TN 972 (1945) 1–84
S. Bergman, Two-dimensional subsonic flows of a compressible fluid and their singularities, Trans. Amer. Math. Soc. 62, 452–498 (1947)
S. Bergman, Integral operators in the theory of linear partial differential equations, Ergeb. Math. No. 23, Springer, Berlin, 1961
S. Bergman, On representation of stream function of subsonic and supersonic flows of compressible fluids, J. Rational Mech. Anal. 4, 883–905 (1955)
S. Bergman, The kernel function and confonnal mapping, Math. Surveys, AMS 5, 1950
S. Bergman and J. G. Herriot, Numerical solution of boundary value problems by the method of integral operators, Numer. Math. 7, 42–65 (1965)
S. Bergman and M. Schiffer, Kernel functions in the theory of partial differential equations of elliptic type, Duke Math. J. 15, 535–566 (1948)
S. Bergman and M. Schiffer, Kernel functions and elliptic differential equations in mathematical physics, Academic Press, New York, 1953
L. Bers, On a method of constructing two-dimensional subsonic flows around closed profiles, NACA Tech. Note No. 969, 1945
L. Bers, An existence theorem in two-dimensional gas dynamics, Proc. of Symposia in Appl. Math. 1, 41–46 (1949)
L. Bers, Mathematical aspects of subsonic and transonic gasdynamics, Surveys in applied mathematics, Wiley and Sons, Inc., New York, 1958
R. Finn, Isolated singularities of solutions of nonlinear partial differential equations, Trans. Amer. Math. Soc. 75, 385–404 (1953)
L. A. Fine, Some qualitative results of a plane subsonic flow, Dissertation, Stanford University, 1965
R. Finn and D. Gilbarg, Asymptotic behavior and uniqueness of plane subsonic flows, Comm. Pure Appl. Math. 10, 23–63 (1957)
D. Gilbarg, Comparison methods in the theory of subsonic flows, J. Rational Mech. Anal. 2, 233–251 (1953)
F. John, General properties of solutions of linear elliptic partial differential equations, Proc. Symposium on Spectral Theory and Differential Problems, Oklahoma A. and M. College, 1951
G. Ludford, The behavior at infinity of the potential function of a two-dimensional subsonic compressible flow, J. Mathematical Phys. 30, 117–30 (1951–2)
R. v. Mises, Mathematical theory of compressible fluid flow, Academic Press, New York, 1958
M. Schiffer, Various types of orthogonalization, Duke Math. J. 17, 329–366 (1950)
J. Stark, Application of Bergman’s integral operators to transonic flows, Int. J. Non-linear Mechanics 1, 17–34 (1966)
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Article copyright:
© Copyright 1968
American Mathematical Society
