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

Article Contents

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

This issue Previous Article Positive solutions for a class of reaction-diffusion systems Next Article Analysis and numerical approximation of a class of two-way diffusions

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: July 2002

Revised: October 2002

Published: November 2003

Abstract / Introduction Related Papers Cited by

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.

Keywords:

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

Citation:

Article Metrics

HTML views() PDF downloads(78) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content