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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