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Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity

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  • In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Suppose that characteristics with constant multiplicity ($>$1) are linearly degenerate only at $u=0$, if there is a genuinely nonlinear simple characteristic which does not have certain "monotonicity" and the initial data possess some decaying properties, we obtain the blow-up result for the $C^1$ solution to the Cauchy problem.
    Mathematics Subject Classification: 35A21, 35L45, 35L60, 35Q72.

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