On the Geometric Blow-Up Mechanism to Scalar Conservation Laws

• 作者: Shikuan Mao Yongqin Liu
• 来源期刊: 现代非线性理论与应用(英文)
• 学科: 数学
• 关键词: BLOW-UP CONSERVATION LAWS Characteristics ENVELOPE
• 年，卷（期）: 2013,（3）
• 页码范围: 161-163
• 页数: 3页
• 分类号: O1

摘要

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.