ABSTRACT
This chapter considers the existence of global weak solutions for the nonlinear hyperbolic conservation laws of quadratic flux with initial data. The system of quadratic flux can be used to approximate any given nonlinear system of two equations near the original point if we represent the nonlinear flux functions by Taylor series first, and then neglect the linear terms and the higher-order small terms. The chapter also provides theorems and proofs for the quadratic flux. It discusses existence of viscosity solutions and Entropy-Entropy flux pairs with related results.
