On the Geometric Blow-Up Mechanism to Scalar Conservation Laws ()
Abstract
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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