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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, where p1, p2,m,α > 0. Among the results, we show that perturbation for the nonnegative solutions propagates with infinite speed in x1-direction and with finite speed in x2- direction if 0 < α < m < p2. We also show that the anisotropic propagation may appear when the convection term is weak, backward, or even missing, if 0 < p1 m < p2, p1 1.
Than Sint Khin
- Journal of Mathematical Analysis and Applications