Asymptotic behavior of solutions to anisotropic conservation laws in two-dimensional space

摘要

In this paper, we investigate the asymptotic behavior of solutions for anisotropic conservation laws in two-dimensional space, provided with step-like initial conditions that approach the constant states u(+/-) (u(-)+/-infinity, respectively. It shows that there is a global classical solution that converges toward the rarefaction wave, ie, the unique entropy solution of the Riemann problem for the nonviscous Burgers' equation in one-dimensional space.