Pointwise stability of shock wave for 2D anisotropic viscous conservation laws with large perturbation

Abstract In this paper, we are interested in the well-posedness of solutions for anisotropic scalar conservation law with large perturbation around the planar shock wave in two dimensional space. It is shown that the Cauchy problem admits a global classical solution by using the classical energy estimates and contraction property, while the initial perturbation is bounded in given space, where we used some new inequalities for anisotropic terms which was imposed in Lemma 2.7. Moreover, we obtain the pointwise estimates of the solutions for fractional order dissipation in y -direction by the formula of Green’s function.