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Microlocal Analysis and Nonlinear Waves pp 1–7Cite as

On the Interactions of Conormal Waves for Semilinear Wave Equations

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 30))

Abstract

Let Ω ⊆ R 3 be an open subset and P be a second order strictly hyperbolic differential operator in Ω. Let S j , 1 ≤ j ≤ n, be smooth characteristic hypersurfaces for P simply tangent along a line L.

This article was written while the author was a visiting lecturer at Rutgers University, New Brunswick.

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References

  1. J.M. Bony, Second Microlocalization and propagation of singularities for semilinear hyperbolic equations, Taniguchi Symp. HERT, Katata (1984), pp. 11–49.

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  2. J.Y. Chemin, Interaction des trois ondes dans les équations semilinéaires strictment hyperboliques d’ordre 2, Thése Université de Paris Sud Centre D’Orsay.

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  5. R. Melrose and A. Sá Barreto, Examples of nondiscreteness for the interaction geometry of semilinear progressing waves in two space dimensions, In Partial Differential Equations, F. Cardoso ed. Lecture notes in Mathematics, Springer Verlag 1988.

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  6. A. Sá Barreto, Interactions of conormal waves for fully semilinear wave equations, Journal of Functional Analysis, vol. 89 No 2 (1990), pp. 233–273.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Purdue University, Mathematical Sciences Building, West Lafayette, IN, 47907, USA

    Antônio Sá Barreto

Authors
  1. Antônio Sá Barreto
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    Michael Beals

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Richard B. Melrose

  3. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1003, USA

    Jeffrey Rauch

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© 1991 Springer-Verlag New York, Inc.

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Barreto, A.S. (1991). On the Interactions of Conormal Waves for Semilinear Wave Equations. In: Beals, M., Melrose, R.B., Rauch, J. (eds) Microlocal Analysis and Nonlinear Waves. The IMA Volumes in Mathematics and its Applications, vol 30. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9136-4_1

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  • DOI: https://doi.org/10.1007/978-1-4613-9136-4_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9138-8

  • Online ISBN: 978-1-4613-9136-4

  • eBook Packages: Springer Book Archive

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