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

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_( ±) , 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.