Study On The Structure Of The Global Weak Entropy Solution For The Initial-boundary Value Problem Of Nonconvex Scalar Conservation Laws

This thesis is concerned with the structure and behaviors of the waves of global weak entropy solutions for the initial-boundary value problems of nonconvex scalar conservation laws. The global weak entropy solutions of the initial-boundary value problems are constructed under the different conditions that the flux function has one inflection point, the initial data is finitely many pieces of constant and the boundary data is constant and that the flux function has finitely many inflection points, the initial data is two pieces of constant and the boundary data is constant. Furthermore, we describe the interaction of the elementary waves with the boundary and clarify the behaviors of the waves nearby the boundary. Compared with the initial-boundary value problem for strictly convex scalar conservation laws, the weak entropy solutions of the initial-boundary value problems for nonconvex scalar conservation laws include the following new interaction types: a rarefaction wave collides with the boundary and the boundary will reflect a centered wave including a contact or non-contact shock wave or furcated shock waves; a contact or non-contact shock wave collides with the boundary and a centered wave including a contact or non-contact shock wave or furcatedshock waves will rebound from the boundary simultaneously or later.