# American Institute of Mathematical Sciences

October  2010, 14(3): 1211-1236. doi: 10.3934/dcdsb.2010.14.1211

## Anti-shifting phenomenon of a convective nonlinear diffusion equation

 1 School of Mathematics, Jilin University, Changchun 130012, China 2 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China 3 School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China

Received  April 2008 Revised  November 2009 Published  July 2010

This paper concerns a convective nonlinear diffusion equation which is strongly degenerate. The existence and uniqueness of the $BV$ solution to the initial-boundary problem are proved. Then we deal with the anti-shifting phenomenon by investigating the corresponding free boundary problem. As a consequence, it is possible to find a suitable convection such that the discontinuous point of the solution remains unmoved.
Citation: Chunpeng Wang, Jingxue Yin, Bibo Lu. Anti-shifting phenomenon of a convective nonlinear diffusion equation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1211-1236. doi: 10.3934/dcdsb.2010.14.1211
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