Construction Of Global Weak Entropy Solution For An Initial-Boundary Value Problem Of Scalar Conservation Laws With Weak Discontinuous Flux Function

This thesis is concerned with the structure and behaviors of the waves of global weak entropy solutions for an initial-boundary value problems of scalar conservation laws with weak discontinuous flux function.The global weak entropy solutions for the initial-boundary value problems are constructed under the different conditions that the flux function is convex but at its two weak discontinuous points, the initial data is piecewise smooth with finitely many discontinuities and the boundary data is constant and that the flux function is nonconvex but at its two weak discontinuous points, the initial data is finitely many pieces of constant and the boundary data is constant. Furthermore, the interaction of elementary waves and the boundary is described and the behaviors of the waves nearby the boundary are clarified.Compared with the initial value problems of scalar conservation laws with smooth flux function, the global weak entropy solutions for the initial-boundary value problems of scalar conservation laws with weak discontinuous flux function include the following new interaction types: a rarefaction wave collides with the boundary and is absorbed compltetely or partially by the boundary; a rarefaction wave collides with the boundary and the boundary will reflect a contact or non-contact shock wave; a contact or non-contact shock wave collides with the boundary and is absorbed by the boundary; a contact or non-contact shock wave collides with the boundary and a new non-contact shock will rebound from the boundary simultaneously or later.