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On the Geometric Blow-Up Mechanism to Scalar Conservation Laws
School of Mathematics and Physics, North China Electric Power University, Beijing, China
School of Mathematics and Physics, North China Electric Power University, Beijing, China
- 1 School of Mathematics and Physics, North China Electric Power University, Beijing, China
- 2 School of Mathematics and Physics, North China Electric Power University, Beijing, China
International Journal of Modern Nonlinear Theory and Application·Volume 02 (2013)·Pages 161–163·Published 19 August 2013·DOI10.4236/ijmnta.2013.23021
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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.
KeywordsBlow-UpConservation LawsCharacteristics Envelope
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