Mechanism of the Formation of Singularities to the Goursat Problem for Diagonal Systems with Linearly Degenerate Characteristic Fields
Received:November 02, 2010  Revised:November 20, 2010
Key Word: formation of singularity   Goursat problem   global $C^1$ solution   quasilinear hyperbolic system of diagonal form   linearly degenerate characteristic   weakly discontinuous solution.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10926162), the Fundamental Research Funds for the Central Universities (Grant No.2009B01314) and the Natural Science Foundation of Hohai University (Grant No.2009428011).
Author NameAffiliation
Yong Fu YANG Department of Mathematics, College of Sciences, Hohai University, Jiangsu 210098, P. R. China 
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      For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the $C^1$ norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of $C^1$ classical solution to the Goursat problem with $C^1$ compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with $C^0$ compatibility conditions at the origin.
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