Two Dimensional Riemann Problem For Scalar Conservation Laws With Nonconvex Assumptions

In this paper,we mainly study the Riemann problem of two dimensional nonconvex conservation law equations,and give some Riemann solutions of two dimensional nonconvex conservation law equations.This paper is divided into three chapters.In the first chapter,we briefly introduce the research history of two-dimensional scalar conservation law equations related to this paper,and describe the cases of Riemann solutions under different conditions that have been considered and the cases considered in this paper.In the second chapter,the generalized characteristic method adopted in this paper is introduced,which mainly introduces rarefaction waves,shock waves and entropy conditions.In chapter 3,the Riemann solution of the two-dimensional scalar conservation law equation under the nonconvex condition is obtained by using the generalized characteristic method.The specific approach is to consider the Riemann problem of the initial value disturbed in one dimension,obtain the fundamental waves in four directions at infinity in two dimensions,and then consider the interaction between the fundamental waves in four directions.Finally,the shape of the solution of the whole self-similar solution plane is obtained by combining the various waves,and the Riemann solution of the conservation law equation we are considering is obtained.