A two-dimensional glimm type scheme on cauchy problem of two-dimensional scalar conservation law

In this paper, we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law {∂tu+∂xf(u)+∂yg(u)=0,u(x,y,0)=u0(x,y). In which initial data can be unbounded. Although the existence and uniqueness of the weak entropy solution are obtained, little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation. So we construct such scheme in our paper and get some new results.