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  1. University of Mandalay
  2. Department of Mathematics

Propagation property for anisotropic nonlinear diffusion equation with convection

http://hdl.handle.net/20.500.12678/0000000658
56d922db-d4fd-4ee7-9858-ba20a65ebd7f
52d44aa2-8375-407f-8eef-756db13e8ecd
Publication type Journal article
Upload Type Publication
Title
Propagation property for anisotropic nonlinear diffusion equation with convection
en
Publication date 2009
Authors
Than Sint Khin
Ning Su
Description
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.
Keywords
Anisotropic nonlinear diffusion
Journal articles
354
Journal of Mathematical Analysis and Applications
Conference papaers
Books/reports/chapters
Thesis/dissertations
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