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Singularities of solutions for nonlinear hyperbolic equations of second order

  • Mikio Tsuji
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)

Abstract

We consider the Cauchy problem for nonlinear hyperbolic partial differential equations of second order. Then the Cauchy problem does not generally admit a classical solution in the large, that is to say, singularities generally appear in finite time. The typical example of singularity is “shock wave”. Our problem is to extend the solution beyond the singularities. Though there are many papers concerning this subject, the existence and uniqueness of weak solution is even now unsolved. In this talk we consider the above problem from geometrical point of view.

Keywords

Weak Solution Cauchy Problem Contact Structure Nonlinear Wave Equation Jump Discontinuity 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Mikio Tsuji
    • 1
  1. 1.Dept. of Math.Kyoto Sangyo UniversityKamigamo, Kita-ku, kyotoJapan

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