TITLE:
Global Solution of a Nonlinear Conservation Law with Weak Discontinuous Flux in the Half Space
AUTHORS:
Xiaoqian Li, Jing Zhang
KEYWORDS:
Nonlinear Conservation Laws with Weak Discontinuous Flux, Initial-Boundary Value Problem, Shock Wave, Rarefaction Wave, Contact Discontinuity, Interaction, Structure of Global Weak Entropy Solution
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.8 No.4,
December
29,
2018
ABSTRACT: 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.