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

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 ± , u m are three given constants satisfying u m = u + ≠ u - or u m = u - ≠ u + , and the flux function f is a given continuous function with a weak discontinuous point u d . 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 ' - ( u d ) > f ' + ( u d ) . 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.