J. Smoller, “Shock Waves and Reaction-Diffusion Equations,” Springer Verlag, New York, Heidelberg, Berlin, 1983. doi:10.1007/978-1-4684-0152-3
has been cited by the following article:
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.