Global Solution of a Nonlinear Conservation Law with Weak Discontinuous Flux in the Half Space

• 作者: Jing Zhang Xiaoqian Li
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: NONLINEAR Conservation Laws with WEAK Discontinuous Flux Initial-Boundary Value Problem Shock WAVE RAREFACTION WAVE Contact Discontinuity Interaction Structure of Global WEAK Entropy Solution
• 年，卷（期）: 2018,（4）
• 页码范围: 326-342
• 页数: 17页
• 分类号: O1

摘要

This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.