We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution. © 2004 American Mathematical Society.
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 1 Mar 2005|
- Asymptotic behavior
- Degenerate parabolic equation
- Diffusion equation
- Entropy dissipation