Abstract
This lecture was intended as an introduction to some of the recent progress in characterizing those linear partial differential operators which are hyperbolic in the sense that the Cauchy problem is locally well-posed in distributions or in C∞. Only single differential operators are considered, the same problems for determined systems are less well understood.
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References
V.Ya. Ivrii, Sufficient conditons for regular and completely regular hyperbolicity. Trudy Moskov. Obsč. 33 (1975), 1–65.
L. Hormander, Linear Partial Differential Operators. Springer-Verlag, New York, 1969. L. Svensson, Necessary and sufficient conditions for the hyperbolicity of polynomials with hyperbolic principal part. Ark. Mat. 8 (1969), 145–162.
F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators. Plenum, New York, 1980. M. Taylor, Pseudodifferential Operators. Princeton University Press, Princeton, 1980. J.J. Duistermaat & L. Hörmander, Fourier integrals operators II. Acta Math. 128 (1972), 183-269.
V.Ya. Ivrii & V.M. Petkov, Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations, Uspechi Mat. Nauk 29 (1974), 3–70. L. Hormander, The Cauchy problem for differential equations with double characteristics. J. d’analyse math. 32 (1977), 188-196. N. Iwasaki, Cauchy problems for effectively hyperbolic equations (preprint). R.B. Melrose, The Cauchy problem for effectively hyperbolic operators. To appear.
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© 1984 Springer Science+Business Media New York
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Melrose, R. (1984). The Cauchy Problem and Propagation of Singularities. In: Chern, S.S. (eds) Seminar on Nonlinear Partial Differential Equations. Mathematical Sciences Research Institute Publications, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1110-5_11
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DOI: https://doi.org/10.1007/978-1-4612-1110-5_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7013-3
Online ISBN: 978-1-4612-1110-5
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