IJMNTA  Vol.2 No.3 , September 2013
On the Geometric Blow-Up Mechanism to Scalar Conservation Laws

The focus of this article is on the geometric mechanism for the blow-up of solutions to the initial value problem for scalar conservation laws. We prove that the sufficient and necessary condition of blow-up is the formation of characteristics envelope. Whether the solution blows up or not relates to the topology structure of a set dominated by initial data. At last we take Burger’s equation as an example to verify our main theorem.

Cite this paper
S. Mao and Y. Liu, "On the Geometric Blow-Up Mechanism to Scalar Conservation Laws," International Journal of Modern Nonlinear Theory and Application, Vol. 2 No. 3, 2013, pp. 161-163. doi: 10.4236/ijmnta.2013.23021.
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