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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