We prove a lower bound on the rate of relaxation to equilibrium in the H1 norm for a thin film equation. We find a two stage relaxation, with power law decay in an initial interval, followed by exponential decay, at an essentially optimal rate, for large times. The waiting time until the exponential decay sets in is explicitly estimated.
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
- Lyapunov functional
- Thin films