Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Anti-shifting phenomenon of a convective nonlinear diffusion equation

Pages: 1211 - 1236, Volume 14, Issue 3, October 2010      doi:10.3934/dcdsb.2010.14.1211

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Chunpeng Wang - School of Mathematics, Jilin University, Changchun 130012, China (email)
Jingxue Yin - School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China (email)
Bibo Lu - School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China (email)

Abstract: 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.

Keywords:  strong degeneracy, convective, $BV$ solution, anti-shifting.
Mathematics Subject Classification:  Primary: 35R35; Secondary: 35K55.

Received: April 2008;      Revised: November 2009;      Available Online: July 2010.