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Hyperbolic Differential Equations and Wave Propagation

Published online by Cambridge University Press:  20 November 2018

G. F. D. Duff*
Affiliation:
Dept. of Mathematics, University of Toronto, Toronto, Ont. M5L 1A1
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Mr. President, ladies and gentlemen, I have had great pleasure in accepting the invitation to deliver this tenth Jeffery-Williams lecture. As one of that generation who were strongly influenced by Ralph Jeffery and Lloyd Williams, I also appreciate the challenge of maintaining the high standard that these lectures named in their honour have established. May I also say that the lecture earlier this morning by Professor Dieudonnè was certainly fortunate for us.

Type
Jeffery-Williams Lecture, 1977
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Amerio, L. and Prouse, G., Almost periodic functions and functional equations, New York, 1971, 184.p.Google Scholar
2. Atiyah, M.F., Bott, R., and Gårding, L., Lacunas for hyperbolic differential equations with constant coefficients, I Acta Math. 124 (1970), 109-189, II Acta Math. 131 (1973), 145-206.Google Scholar
3. Bondi, H., Waves on the surface of a compressible liquid, Proc. Camb. Phil. Soc. 43 (1947), 75-95.Google Scholar
4. Chazarain, J., Le problème de Cauchy pour les opérateurs hyperboliques, non-nécessairement stricts, qui satisfont à la condition de Levi, C. R. Acad. Sci. Paris, Ser. A-B, 273 (1971), A1218-A1221.Google Scholar
5. Courant, R., Methods of Mathematical Physics, 2nd edn., vol. II, Ch. 6, New York, 1962.Google Scholar
6. Duff, G. F. D., On the Riemann matrix of a hyperbolic system, M. R. C. Technical Report 246 (1961), 58 pp., Madison, Wisconsin.Google Scholar
7. Duff, G. F. D., Hyperbolic differential equations and waves, in Boundary Value Problems for Linear Evolution Partial Differential Equations, ?d. Garnir, H. G., Dordrecht, (1977), 27-156.Google Scholar
8. Duff, G. F. D., Mathematical Problems of Tidal Energy, S?minaires IRIA, Analyse et Control le de Syst?mes, 1973, 97-174.Google Scholar
9. G?rding, L., Cauchy's problem for hyperbolic equations, Univ. of Chicago lecture notes, 151.p. (1958).Google Scholar
10. G?rding, L., The mixed problem for hyperbolic equations, in press.Google Scholar
11. Gelfand, I.M. and Shilov, G.E., Generalized Functions, Vol. I, Properties and Operations, 423.pp., trans. 1964, Academic Press.Google Scholar
12. Herglotz, G., Leipzig. Ber Säch., Akad. Wiss. Math. Phys. Kl, I, 78 (1926), 93-106, II, 80 (1928), 6-14.Google Scholar
13. Hormander, L., Linear partial differential operators, Berlin (1963), 284.pp.Google Scholar
14. Ikawa, M., Sur les probl?mes mixtes pour Vequation des ondes, Publ. R.I.M.S., Kyoto Univ. 10 (1975), 669-690.Google Scholar
15. Leray, J., Hyperbolic Differential Equations. Lecture Notes, Institute for Advanced Study, 1952.Google Scholar
16. Ludwig, D., Singularities of Superpositions of Distributions, Pac. J. Math. 15 (1965), 215-239.Google Scholar
17. Mizohata, S. and Ohya, Y., Sur la condition d'hyperbolicité pour des équations à caractéristiques multiples, II, Jap. J. Math., Vol. 40 (1971), 63-104.Google Scholar
18. Petrowsky, I., On the diffusion of waves and the lacunas for hyperbolic equations, Mat. Sbornik, 8612(59) (1945), 289-370.Google Scholar
19. Russell, D.L., Controllability theory for hyperbolic and parabolic partial differential equations, Studies in Applied Mathematics, 52 (1973), 189-211.Google Scholar
20. Tsuji, M., Propagation of the singularities for hyperbolic equations with constant coefficients, Japan J. Math. 2 (1976), 361-410.Google Scholar
21. Wakabayashi, S., Analytic Wave Front Sets of the Riemann Functions of Hyperbolic Mixed Problems in a Quarter Space, (to appear).Google Scholar
22. Zeman, M., The Well-posedness of the Cauchy Problem for Partial Differential Equations with Multiple Characteristics, Comm. P.D.E. 2 (1977), 223-250.Google Scholar
23. Dieudonné, J., Recent History of the theory of Linear Partial Differential Equations, lecture sponsored by the Canadian Society for History and Philosophy of Mathematics, 1977.Google Scholar