Propagation property for anisotropic nonlinear diffusion equation with convection

We consider propagation property for anisotropic diffusion equation with convection in 2 dimension,∂t(um)−∂x1(|∂x1u|p1−1∂x1u)−∂x2(|∂x2u|p2−1∂x2u)+uα−1∂x1u=0,∂t(um)−∂x1(|∂x1u|p1−1∂x1u)−∂x2(|∂x2u|p2−1∂x2u)+uα−1∂x1u=0, where p1,p2,m,α>0p1,p2,m,α>0. Among the results, we show that perturbation for the nonnegative solutions propagates with infinite speed in x1x1-direction and with finite speed in x2x2-direction if 0<α