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The lifespan of classical solutions of non-linear hyperbolic equations

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Pseudo-Differential Operators

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1256))

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References

  1. R. DiPerna and A. Majda, The validity of nonlinear geometric optics for weak solutions of conservation laws. Report PAM-235, June 1984, Center for pure and applied mathematics, University of California, Berkeley.

    Google Scholar 

  2. L. Hörmander, On Sobolev spaces associated with some Lie algebras. Report 4, 1985, Institute Mittag-Leffler.

    Google Scholar 

  3. F. John, Formation of singularities in one-dimensional non-linear wave propagation. Comm.Pure Appl.Math. 27(1974), 377–405.

    Article  MathSciNet  MATH  Google Scholar 

  4. -, Blowup of radial solutions of utt=c2(ut) u in three space dimensions. Preprint 1984.

    Google Scholar 

  5. -, A lower bound for the life span of solutions of nonlinear wave equations in three space dimensions. Preprint 1986.

    Google Scholar 

  6. F. John and S. Klainerman, Almost global existence to nonlinear wave equations in three space dimensions. Comm. Pure Appl. Math. 37(1984), 443–455.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation. Preprint 1984.

    Google Scholar 

  8. -, Global existence for nonlinear wave equations. Comm. Pre Appl. Math. 33(1980), 43–101.

    Article  MathSciNet  MATH  Google Scholar 

  9. -, The null condition and global existence to nonlinear wave equations. Preprint 1985.

    Google Scholar 

  10. -, Long time behaviour of solutions to nonlinear wave equations. Proc. Int. Congr. Math., Warszawa 1983, 1209–1215.

    Google Scholar 

  11. P.D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Regional conf. series in applied mathematics 11, SIAM 1973.

    Google Scholar 

  12. -, Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10(1957), 227–241.

    MathSciNet  MATH  Google Scholar 

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Authors
  1. Lars Hörmander
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Heinz O. Cordes Bernhard Gramsch Harold Widom

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© 1987 Springer-Verlag

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Hörmander, L. (1987). The lifespan of classical solutions of non-linear hyperbolic equations. In: Cordes, H.O., Gramsch, B., Widom, H. (eds) Pseudo-Differential Operators. Lecture Notes in Mathematics, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077745

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  • DOI: https://doi.org/10.1007/BFb0077745

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17856-9

  • Online ISBN: 978-3-540-47886-7

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