TITLE:
On the Geometric Blow-Up Mechanism to Scalar Conservation Laws
AUTHORS:
Shikuan Mao, Yongqin Liu
KEYWORDS:
Blow-Up; Conservation Laws; Characteristics Envelope
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.2 No.3,
August
19,
2013
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.