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Volume 18, Issue 4
Formation of Singularities for Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity

Yumei Xu

J. Part. Diff. Eq., 18 (2005), pp. 355-370.

Published online: 2005-11

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  • Abstract

In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity (> 1), a blow-up result is obtained for the C¹ solution to the Cauchy problem under the assumptions where there is a simple genuinely nonlinear characteristic and the initial data possess certain weaker decaying properties.

  • Keywords

Quasilinear hyperbolic systems Cauchy problem formation of singularity life-span

  • AMS Subject Headings

35A21 35L45 35L60 35Q72

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-18-355, author = {Yumei Xu }, title = {Formation of Singularities for Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity}, journal = {Journal of Partial Differential Equations}, year = {2005}, volume = {18}, number = {4}, pages = {355--370}, abstract = {

In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity (> 1), a blow-up result is obtained for the C¹ solution to the Cauchy problem under the assumptions where there is a simple genuinely nonlinear characteristic and the initial data possess certain weaker decaying properties.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5370.html} }
TY - JOUR T1 - Formation of Singularities for Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity AU - Yumei Xu JO - Journal of Partial Differential Equations VL - 4 SP - 355 EP - 370 PY - 2005 DA - 2005/11 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5370.html KW - Quasilinear hyperbolic systems KW - Cauchy problem KW - formation of singularity KW - life-span AB -

In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity (> 1), a blow-up result is obtained for the C¹ solution to the Cauchy problem under the assumptions where there is a simple genuinely nonlinear characteristic and the initial data possess certain weaker decaying properties.

Yumei Xu . (2005). Formation of Singularities for Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity. Journal of Partial Differential Equations. 18 (4). 355-370. doi:
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