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

Libin Wang

doi:10.3934/cpaa.2003.2.77

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2003, Volume 2, Issue 1: 77-89. Doi: 10.3934/cpaa.2003.2.77

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

Libin Wang¹

1.
Institute of Mathematics, Fudan University, Shanghai 200433

Received: June 30, 2002

Revised: September 30, 2002

Published: October 2003

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Abstract

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.

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Mathematics Subject Classification: 35A21, 35L45, 35L60, 35Q72.

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