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

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March 2003, 2(1): 77-89. doi: 10.3934/cpaa.2003.2.77

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

1.	Institute of Mathematics, Fudan University, Shanghai 200433, China

Received July 2002 Revised October 2002 Published December 2002

Abstract
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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.

Keywords: Quasilinear hyperbolic system, life-span., Cauchy problem, blow up.

Mathematics Subject Classification: 35A21, 35L45, 35L60, 35Q7.

Citation: Libin Wang. Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Communications on Pure & Applied Analysis, 2003, 2 (1) : 77-89. doi: 10.3934/cpaa.2003.2.77

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