Anti-shifting phenomenon of a convective nonlinear diffusion equation (Q612902)

The authors consider the following convective nonlinear diffusion equation which is strongly degenerate \[ \frac{\partial u}{\partial t} = \frac{\partial}{\partial x}\psi \left(\frac{\partial u}{\partial x} \right) + \frac{\partial}{\partial x}A(x,t,u) + B(x,t,u),\quad (x,t)\in (-l,l)\times (0,T). \] The existence and uniqueness of the bounded variational solution to the initial-boundary problem are proved. Then the authors deal with the anti-shifting phenomenon by investigating the corresponding free boundary problem. As a consequence, a suitable convection is found such that the discontinuous point of the solution remains unmoved.