Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux

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.

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

“…For such an initial-boundary value problem (2)- (4), under the conditions of (A 1 ) and (A 2 ), the global weak entropy solution was constructed in [1] for the case of ( ) ( )…”