A note on a parabolic equation with nonlinear dynamical boundary condition
- Sprekels, Jürgen
- Wu, Hao
2010 Mathematics Subject Classification
- 35B40 35B41 35B45
- Parabolic equation, dynamical boundary condition, global attractor, convergence to equilibrium, Lojasiewicz-Simon inequality
We consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-called Wentzell boundary condition. First, we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we derive a suitable Łojasiewicz-Simon type inequality to show the convergence of global solutions to single steady states as time tends to infinity under the assumption that the nonlinear terms f, g are real analytic. Moreover, we provide an estimate for the convergence rate.
- Nonlinear Anal., 72 (2010) pp. 3028--3048.