TITLE:
Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux
AUTHORS:
Yihong Dai, Jing Zhang
KEYWORDS:
Scalar Conservation Laws with Weak Discontinuous Flux, Initial-Boundary Value Problem, Elementary Wave, Interaction, Structure of Global Weak Entropy Solution
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.4,
December
14,
2017
ABSTRACT: This
paper is concerned with the initial-boundary value problem of scalar conservation
laws with weak discontinuous flux, whose initial data are a function with two
pieces of constant and whose boundary data are a constant function.
Under the condition that the flux function has a finite number of weak discontinuous
points, by using the structure of weak entropy solution of the corresponding
initial value problem and the boundary entropy condition developed by
Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy
solution for this initial-boundary value problem, and by investigating the
interaction of elementary waves and the boundary, we clarify the geometric
structure and the behavior of boundary for the weak entropy solution.