March  2009, 8(2): 757-768. doi: 10.3934/cpaa.2009.8.757

Mechanism of the formation of singularities for diagonal systems with linearly degenerate characteristic fields

1. 

Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098, Jiangsu, China

Received  February 2008 Revised  September 2008 Published  December 2008

For inhomogeneous diagonal system with distinct characteristics or with characteristics with constant multiplicity, under the assumption that the system is linearly degenerate and the $C^1$ norm of the initial data is bounded, we show that the mechanism of the formation of singularities of classical solution to its Cauchy problem must be of ODE type. Similar results are also obtained for corresponding mixed initial-boundary value problems on a semi-unbounded domain.
Citation: Yong-Fu Yang. Mechanism of the formation of singularities for diagonal systems with linearly degenerate characteristic fields. Communications on Pure & Applied Analysis, 2009, 8 (2) : 757-768. doi: 10.3934/cpaa.2009.8.757
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