Formation of singularities to quasi-linearhyperbolic systems with initial data of small BV norm

Wen-Rong Dai

doi:10.3934/dcds.2012.32.3501

Article Contents

2012, Volume 32, Issue 10: 3501-3524. Doi: 10.3934/dcds.2012.32.3501

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Formation of singularities to quasi-linear hyperbolic systems with initial data of small BV norm

Wen-Rong Dai^1,

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234

Received: April 30, 2011

Revised: October 31, 2011

Published: September 2012

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Abstract

In this paper, we investigate the formation of singularities of the classical solution to the Cauchy problem of quasi-linear hyperbolic system and give a sharp limit formula for the lifespan of the classical solution. It is important that we only require that the initial data are sufficiently small in the $L^1$ sense and the BV sense.

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Mathematics Subject Classification: Primary: 35L45, 35L60; Secondary: 35L40.

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