FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS VIA LAX-OLEINIK FORMULA

• 作 者: 王泽军 张琦
• 机 构: DepartmentofMathematics
• 出 处: 数学物理学报:B辑英文版
• 发表日期: 2019年1期
• 关键词: SCALAR conservation law Lax-Oleinik FORMULA RIEMANN problem asymptotic behavior
• 基金项目: supported in part by NSFC(11671193),the Fundamental Research Funds for the Central Universities(NE2015005),supported in part by NSFC(11271182 and 11501290).

In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law u_t + F(u)_x = 0. First, we prove a simple but useful property of Lax-Oleinik formula(Lemma 2.7). In fact, denote the Legendre tr