| 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 Words:
formation of singularity Goursat problem global $C^1$ solution quasilinear hyperbolic system of diagonal form linearly degenerate characteristic weakly discontinuous solution.
|
| Fund Project: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). |
|
| Hits: 2877 |
| Download times: 1751 |
| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.01.003 |
| View Full Text View/Add Comment |
